{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":42264,"title":"calculate the tangent of angle in radians","description":"Calculate the tangent of angle in degrees","description_html":"\u003cp\u003eCalculate the tangent of angle in degrees\u003c/p\u003e","function_template":"function y = tangent1(x)\r\n  y = tand(x);\r\nend","test_suite":"%%\r\nx = 90;\r\ny = inf;\r\nassert(isequal(tangent1(x),y))\r\n\r\n%%\r\nx = 45;\r\ny = 1;\r\nassert(isequal(tangent1(x),y))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":38003,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":150,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-04-24T10:05:35.000Z","updated_at":"2026-02-12T16:53:26.000Z","published_at":"2015-04-24T10:05:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the tangent of angle in degrees\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46034,"title":"Construct the Seidel-Entringer-Arnold triangle","description":"Several problems in Cody ask us to construct part or all of triangles in which entries follow a pattern. Cody Problems \u003chttps://www.mathworks.com/matlabcentral/cody/problems/37 37\u003e, \u003chttps://www.mathworks.com/matlabcentral/cody/problems/1463 1463\u003e, \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44037 44037\u003e, and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44904 44904\u003e involve Pascal's triangle, which consists of the binomial coefficients, and Cody Problem \u003chttps://www.mathworks.com/matlabcentral/cody/groups/31/problems/1845 1845\u003e extends Pascal's triangle to a pyramid. Cody Problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/45423-bernoulli-s-triangle 45460\u003e involves the Bernoulli triangle, which consists of partial sums of the binomial coefficients. \r\n\r\nThis problem deals with the Seidel-Entringer-Arnold triangle (also called the Euler-Bernoulli triangle and the secant-tangent triangle). The first eight layers are\r\n\r\n  \r\n                         1\r\n                      0      1\r\n                  1      1      0\r\n               0      1      2      2\r\n           5      5      4      2      0\r\n        0      5     10     14     16     16\r\n    61    61     56     46     32     16      0\r\n  0    61    122    178    224    256    272    272   \r\n  \r\nThe name \"secant-tangent triangle\" arises because the sides contain the coefficients in the Taylor series for sec(x) and tan(x):\r\n\r\n sec(x) = 1 + 1x^2/2! + 5x^4/4! + 61x^6/6! + ...\r\n tan(x) = 1x + 2x^3/3! + 16x^5/5! + 272x^7/7! + ...\r\n\r\nConstruct the nth layer of this triangle. \r\n\r\nHint: Use the boustrophedon (or ox-plowing) rule. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 510.567px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 255.283px; transform-origin: 407px 255.283px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 359.033px 7.8px; transform-origin: 359.033px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSeveral problems in Cody ask us to construct part or all of triangles in which entries follow a pattern. Cody Problems\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/37\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e37\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/1463\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"perspective-origin: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; \"\u003e1463\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44037\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e44037\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44904\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e44904\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 271.55px 7.8px; transform-origin: 271.55px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involve Pascal's triangle, which consists of the binomial coefficients, and Cody Problem\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/31/problems/1845\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e1845\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e extends Pascal's triangle to a pyramid. Cody Problem\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45423-bernoulli-s-triangle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e45460\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 191.383px 7.8px; transform-origin: 191.383px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves the Bernoulli triangle, which consists of partial sums of the binomial coefficients.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.033px 7.8px; transform-origin: 382.033px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem deals with the Seidel-Entringer-Arnold triangle (also called the Euler-Bernoulli triangle and the secant-tangent triangle). The first eight layers are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 163.467px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 81.7333px; transform-origin: 404px 81.7333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100.1px 8.25px; transform-origin: 100.1px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                         1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 115.5px 8.25px; transform-origin: 115.5px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                      0      1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 127.05px 8.25px; transform-origin: 127.05px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                  1      1      0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 142.45px 8.25px; transform-origin: 142.45px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e               0      1      2      2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e           5      5      4      2      0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 8.25px; transform-origin: 169.4px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        0      5     10     14     16     16\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 180.95px 8.25px; transform-origin: 180.95px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    61    61     56     46     32     16      0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 196.35px 8.25px; transform-origin: 196.35px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  0    61    122    178    224    256    272    272\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.917px 7.8px; transform-origin: 333.917px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe name \"secant-tangent triangle\" arises because the sides contain the coefficients in the Taylor series for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sec(x)\" style=\"width: 42px; height: 18.5px;\" width=\"42\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"tan(x)\" style=\"width: 41.5px; height: 18.5px;\" width=\"41.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.05px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.0333px; text-align: left; transform-origin: 384px 18.0333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e       \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sec(x) = 1 + 1x^2/2! + 5x^4/4! + 61x^6/6! + ...\" style=\"width: 226px; height: 36px;\" width=\"226\" height=\"36\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.05px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.0333px; text-align: left; transform-origin: 384px 18.0333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e       \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"tan(x) = 1x + 2x^3/3! + 16x^5/5! + 272x^7/7! + ...\" style=\"width: 247.5px; height: 36px;\" width=\"247.5\" height=\"36\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.85px 7.8px; transform-origin: 117.85px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConstruct the nth layer of this triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.883px 7.8px; transform-origin: 152.883px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Use the boustrophedon (or ox-plowing) rule.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = SeidelEntringerArnold(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = 1;\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%%\r\nn = 3;\r\ny_correct = [1 1 0];\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%%\r\nn = 5;\r\ny_correct = [5 5 4 2 0];\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%%\r\nn = 8;\r\ny_correct = [0 61 122 178 224 256 272 272];\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%% \r\nn = 13;\r\ny_correct = [2702765 2702765 2652244 2551202 2401024 2204480 1965664 1689872 1383424 1053440 707584 353792 0];\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%%\r\nn = 10;\r\ny = SeidelEntringerArnold(n);\r\ns = sum(y); \r\nv = round(var(y));\r\nd = y([4 6 9]) - y([2 5 7]);\r\ns_correct = 50521;\r\nv_correct = 8277369;\r\nd_correct = [2709 1024 816];\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(v,v_correct) \u0026\u0026 isequal(d,d_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-07-07T19:46:14.000Z","updated_at":"2025-12-15T13:25:13.000Z","published_at":"2020-07-08T01:44:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSeveral problems in Cody ask us to construct part or all of triangles in which entries follow a pattern. Cody Problems\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/37\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e37\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/1463\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1463\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44037\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e44037\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44904\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e44904\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involve Pascal's triangle, which consists of the binomial coefficients, and Cody Problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/31/problems/1845\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1845\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e extends Pascal's triangle to a pyramid. Cody Problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45423-bernoulli-s-triangle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e45460\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves the Bernoulli triangle, which consists of partial sums of the binomial coefficients.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem deals with the Seidel-Entringer-Arnold triangle (also called the Euler-Bernoulli triangle and the secant-tangent triangle). The first eight layers are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[                         1\\n                      0      1\\n                  1      1      0\\n               0      1      2      2\\n           5      5      4      2      0\\n        0      5     10     14     16     16\\n    61    61     56     46     32     16      0\\n  0    61    122    178    224    256    272    272]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe name \\\"secant-tangent triangle\\\" arises because the sides contain the coefficients in the Taylor series for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sec(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sec(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"tan(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\tan(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sec(x) = 1 + 1x^2/2! + 5x^4/4! + 61x^6/6! + ...\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sec(x) = 1 + 1\\\\frac{x^2}{2!}+5\\\\frac{x^4}{4!}+61\\\\frac{x^6}{6!}+\\\\ldots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"tan(x) = 1x + 2x^3/3! + 16x^5/5! + 272x^7/7! + ...\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\tan(x) = 1x + 2\\\\frac{x^3}{3!}+16\\\\frac{x^5}{5!}+272\\\\frac{x^7}{7!}+\\\\ldots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConstruct the nth layer of this triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Use the boustrophedon (or ox-plowing) rule.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58872,"title":"Find the Points Tangent to a Circle from an External Point ","description":"From a point where do the lines touch a circle tangentially?. The loldrup solution may provide some guidance and alternate method. I will elaborate a more reference frame modification geometric solution utilizing Matlab specific functions, rotation matrix, and translation matrix.\r\nGiven point(px,py) and circle [cx,cy,R] return the circle points [x3 y3;x4 y4] where lines thru the point are tangential to the circle.  The line ([px,py],[x3,y3]) is tangential to circle [cx,cy,R] at circle point [x3,y3]. D\u003eR.\r\nThe below figure is created based upon h=P=distance([cx,cy],[px,py])/2=D/2, translating (cx,cy) to (0,0), and rotating (px,py) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,P]. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\r\nP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(h-Y)^2 = Y^2-h^2+2hY-Y^2=2hY-h^2 thus\r\nY=(R^2-P^2+h^2)/(2h) =(R^2-P^2+P^2)/(2P)=R^2/(2P)=R^2/D\r\nX=+/- (R^2-Y^2)^.5=+/- (R^2-(R^2/(2P))^2)^0.5=+/- R*(1-(R/D)^2)^0.5\r\nThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [cx cy]\r\n\r\n\r\nThis figure shows the point (px,py) rotated onto the Y-axis at position 2P. The circle (cx,cy) has been shifted to the origin with radius R. The green line shows a tangent at (x,y) from (px,py). A second tangent point is at (-x.y). D=2*P","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 952.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 476.25px; transform-origin: 407px 476.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 204px 8px; transform-origin: 204px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFrom a point where do the lines touch a circle tangentially?. The \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://math.stackexchange.com/questions/913239/given-circle-and-point-where-does-the-tangential-line-through-the-point-touch-t\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eloldrup\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e solution may provide some guidance and alternate method. I will elaborate a more reference frame modification geometric solution utilizing Matlab specific functions, rotation matrix, and translation matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven point(px,py) and circle [cx,cy,R] return the circle points [x3 y3;x4 y4] where lines thru the point are tangential to the circle.  The line ([px,py],[x3,y3]) is tangential to circle [cx,cy,R] at circle point [x3,y3]. D\u0026gt;R.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.5px 8px; transform-origin: 366.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe below figure is created based upon h=P=distance([cx,cy],[px,py])/2=D/2, translating (cx,cy) to (0,0), and rotating (px,py) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,P]. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 358px 8px; transform-origin: 358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(h-Y)^2 = Y^2-h^2+2hY-Y^2=2hY-h^2 thus\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188px 8px; transform-origin: 188px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eY=(R^2-P^2+h^2)/(2h) =(R^2-P^2+P^2)/(2P)=R^2/(2P)=R^2/D\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211px 8px; transform-origin: 211px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eX=+/- (R^2-Y^2)^.5=+/- (R^2-(R^2/(2P))^2)^0.5=+/- R*(1-(R/D)^2)^0.5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378px 8px; transform-origin: 378px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [cx cy]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 556.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 278.25px; text-align: left; transform-origin: 384px 278.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 419px;height: 551px\" 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\" data-image-state=\"image-loaded\" width=\"419\" height=\"551\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.5px 8px; transform-origin: 378.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis figure shows the point (px,py) rotated onto the Y-axis at position 2P. The circle (cx,cy) has been shifted to the origin with radius R. The green line shows a tangent at (x,y) from (px,py). A second tangent point is at (-x.y). D=2*P\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n%Find points on circle that when drawn to a point only touches circle at the circle point.\r\n%The line from the circle center to (x3 y3) is orthogonal to the line [(px,py) (x3,y3)]\r\n%A second point (x4,y4) also creates an orthogonal lines intersection\r\n\r\n  D=norm([px-cx py-cy])\r\n  \r\n  %Y=\r\n  %X=\r\n  \r\n  xy=[X Y;-X Y];\r\n \r\n %Rotation Angle: atan2\r\n theta=atan2(px-cx,py-cy); % (X,Y) output radians Neg Left of vert, Pos Right of Vert\r\n \r\n %Rotation Matrix: [cos(t) -sin(t);sin(t) cos(t)]\r\n %Translation matrix: [cx cy]\r\n %Check of (px,py) being regenerated from D, theta, and translation\r\n [pxyD]=[0 D]*[cos(theta) -sin(theta);sin(theta) cos(theta)]+[cx cy]\r\n [px py]\r\n \r\n %xy=\r\n \r\n \r\n  \r\nend %TangentPoints_onCircle","test_suite":"%%\r\nvalid=1;\r\npx=6;py=8;cx=0;cy=0;R=4;\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n\r\n%%\r\nvalid=1;\r\npx=-6;py=-8;cx=2;cy=4;R=6;\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n\r\n%%\r\nvalid=1;\r\npx=6;py=8;cx=1;cy=-2;R=5;\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n\r\n%%\r\nvalid=1;\r\n%px=6;py=8;cx=1;cy=-2;R=5;\r\ncx=-5*rand; cy=-5*rand; R=4+rand;\r\npx=3+2*rand; py=3+2*rand;\r\n[px py cx cy R]\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-12T23:33:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-12T21:15:25.000Z","updated_at":"2023-08-12T23:33:27.000Z","published_at":"2023-08-12T23:33:27.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFrom a point where do the lines touch a circle tangentially?. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://math.stackexchange.com/questions/913239/given-circle-and-point-where-does-the-tangential-line-through-the-point-touch-t\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eloldrup\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e solution may provide some guidance and alternate method. I will elaborate a more reference frame modification geometric solution utilizing Matlab specific functions, rotation matrix, and translation matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven point(px,py) and circle [cx,cy,R] return the circle points [x3 y3;x4 y4] where lines thru the point are tangential to the circle.  The line ([px,py],[x3,y3]) is tangential to circle [cx,cy,R] at circle point [x3,y3]. D\u0026gt;R.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe below figure is created based upon h=P=distance([cx,cy],[px,py])/2=D/2, translating (cx,cy) to (0,0), and rotating (px,py) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,P]. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(h-Y)^2 = Y^2-h^2+2hY-Y^2=2hY-h^2 thus\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eY=(R^2-P^2+h^2)/(2h) =(R^2-P^2+P^2)/(2P)=R^2/(2P)=R^2/D\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eX=+/- (R^2-Y^2)^.5=+/- (R^2-(R^2/(2P))^2)^0.5=+/- R*(1-(R/D)^2)^0.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [cx cy]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"551\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"419\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis figure shows the point (px,py) rotated onto the Y-axis at position 2P. The circle (cx,cy) has been shifted to the origin with radius R. The green line shows a tangent at (x,y) from (px,py). A second tangent point is at (-x.y). 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the tangent of angle in radians","description":"Calculate the tangent of angle in degrees","description_html":"\u003cp\u003eCalculate the tangent of angle in degrees\u003c/p\u003e","function_template":"function y = tangent1(x)\r\n  y = tand(x);\r\nend","test_suite":"%%\r\nx = 90;\r\ny = inf;\r\nassert(isequal(tangent1(x),y))\r\n\r\n%%\r\nx = 45;\r\ny = 1;\r\nassert(isequal(tangent1(x),y))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":38003,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":150,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-04-24T10:05:35.000Z","updated_at":"2026-02-12T16:53:26.000Z","published_at":"2015-04-24T10:05:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the tangent of angle in degrees\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46034,"title":"Construct the Seidel-Entringer-Arnold triangle","description":"Several problems in Cody ask us to construct part or all of triangles in which entries follow a pattern. Cody Problems \u003chttps://www.mathworks.com/matlabcentral/cody/problems/37 37\u003e, \u003chttps://www.mathworks.com/matlabcentral/cody/problems/1463 1463\u003e, \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44037 44037\u003e, and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44904 44904\u003e involve Pascal's triangle, which consists of the binomial coefficients, and Cody Problem \u003chttps://www.mathworks.com/matlabcentral/cody/groups/31/problems/1845 1845\u003e extends Pascal's triangle to a pyramid. Cody Problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/45423-bernoulli-s-triangle 45460\u003e involves the Bernoulli triangle, which consists of partial sums of the binomial coefficients. \r\n\r\nThis problem deals with the Seidel-Entringer-Arnold triangle (also called the Euler-Bernoulli triangle and the secant-tangent triangle). The first eight layers are\r\n\r\n  \r\n                         1\r\n                      0      1\r\n                  1      1      0\r\n               0      1      2      2\r\n           5      5      4      2      0\r\n        0      5     10     14     16     16\r\n    61    61     56     46     32     16      0\r\n  0    61    122    178    224    256    272    272   \r\n  \r\nThe name \"secant-tangent triangle\" arises because the sides contain the coefficients in the Taylor series for sec(x) and tan(x):\r\n\r\n sec(x) = 1 + 1x^2/2! + 5x^4/4! + 61x^6/6! + ...\r\n tan(x) = 1x + 2x^3/3! + 16x^5/5! + 272x^7/7! + ...\r\n\r\nConstruct the nth layer of this triangle. \r\n\r\nHint: Use the boustrophedon (or ox-plowing) rule. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 510.567px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 255.283px; transform-origin: 407px 255.283px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 359.033px 7.8px; transform-origin: 359.033px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSeveral problems in Cody ask us to construct part or all of triangles in which entries follow a pattern. Cody Problems\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/37\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e37\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/1463\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"perspective-origin: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; \"\u003e1463\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44037\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e44037\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44904\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e44904\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 271.55px 7.8px; transform-origin: 271.55px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involve Pascal's triangle, which consists of the binomial coefficients, and Cody Problem\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/31/problems/1845\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e1845\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e extends Pascal's triangle to a pyramid. Cody Problem\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45423-bernoulli-s-triangle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e45460\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 191.383px 7.8px; transform-origin: 191.383px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves the Bernoulli triangle, which consists of partial sums of the binomial coefficients.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.033px 7.8px; transform-origin: 382.033px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem deals with the Seidel-Entringer-Arnold triangle (also called the Euler-Bernoulli triangle and the secant-tangent triangle). The first eight layers are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 163.467px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 81.7333px; transform-origin: 404px 81.7333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100.1px 8.25px; transform-origin: 100.1px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                         1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 115.5px 8.25px; transform-origin: 115.5px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                      0      1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 127.05px 8.25px; transform-origin: 127.05px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                  1      1      0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 142.45px 8.25px; transform-origin: 142.45px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e               0      1      2      2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 154px 8.25px; transform-origin: 154px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e           5      5      4      2      0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 8.25px; transform-origin: 169.4px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        0      5     10     14     16     16\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 180.95px 8.25px; transform-origin: 180.95px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    61    61     56     46     32     16      0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 196.35px 8.25px; transform-origin: 196.35px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  0    61    122    178    224    256    272    272\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.917px 7.8px; transform-origin: 333.917px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe name \"secant-tangent triangle\" arises because the sides contain the coefficients in the Taylor series for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sec(x)\" style=\"width: 42px; height: 18.5px;\" width=\"42\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"tan(x)\" style=\"width: 41.5px; height: 18.5px;\" width=\"41.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.05px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.0333px; text-align: left; transform-origin: 384px 18.0333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e       \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sec(x) = 1 + 1x^2/2! + 5x^4/4! + 61x^6/6! + ...\" style=\"width: 226px; height: 36px;\" width=\"226\" height=\"36\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.05px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.0333px; text-align: left; transform-origin: 384px 18.0333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e       \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAe8AAABICAYAAADf530vAAAN4ElEQVR4nO2dPY7rOhKFTzA7cD6BN2BgYgcvNjC545c4fJk3MHD+Iq/B8UTeQyezgF6Dt9ATyAcusSX+idTv+QDh4rZlSyIpHlaxWASEEEIIIYQQQgghhBBCCCGEEEIIIYTwswdwfB9iPI7OcQJwnvSORBc7/K4rexymuzUhxBbZAXgC+DHHE42Yi7oc0C53Hir7+XFBd13xuEx3a0KILfIEcEMj4jsAdzSd0X3Km9oIdzRlLwtu/nyj2yt1hQZcQoiROaIRD8sOTWf0Nf7tbIo9mnLeTX0jIsgB/VMZX2gGwEIIMTk/+C3qoiw3fKYorpDFvUQ4ALtOfSNCCHFG4yKURViXb/yeN71C5b4kOA+ugZcQYlJOAF5oOiWJyDic0A4YlBW3HJ5oBmFCCDEJOzRuXGsNym0+Lmc05f6CBk5LgLEhGmwJIWaBXRIjERmXB5pyP019IyIIB1vKiyCEmA1c/iIRGZcTVO5L4YHGSyKEELPhCInIFLDcZc3NnxeUC0EIUYEDukWAaR59SSUoInKbpzOk3OmKFePSlxyHKYPd90AeEiFEUU74uPM4b207mLP57ImmU+rqtO7v3xFxpJb7v9At5Mx2J+pzQTvK/4V2fdzQH7zJLIRCCFEECjGTR/zgI8JcBnZ7//vAZ277ab57QZM1SlZ3PKnlTtH4fn/OtLQaMI0H64zeDpuf/IbmHbg7fyesR7EB+iycXJQUQISgQHyhaS+uZYH3/+/vc2n1ab51GLHlfoPKfS5QvO9oBlO+tdt7NHWm+toA3LWppODeIPea8EOrmkKi+bk0uFFLKir35WE9IVpnLwDUEW5ywzqjHc/Y1g49OzQd/PV9lHp+Bp1ZF+6a2WPYPtgntL0QuVs8bqHcWdZss3T9+86/Jhx97T/1urHYAZe29hQAmpF3zcbwqPz7Y8Kc2lvKFXxBO8jJzXM9lC1kS6PrP1csr/jUgU84UlhruTMTX1d7faHfy3Dt+U7f77iCnHvdWOyAS56SEZh7IXNOqyZ7NI13yWJ3xO9NGpb8PLGwQ3vhY+25HdOQzn+HT7muccvCrg49Rbz3aAbXXZHGQ+9rreVu3ctPfMrPHl39si2PvoPndHkTc68by8H8jtKdVoZLM+YKo07HCGq4Yrl7L5/wcX0xNeQcxZtrdEvVJzuLG9pWxg6/rZTcsrDlOeWaba6VLV2n3EbTdryxfQIDyTgvXbJs1lruTJvrTk3s0X5md0c6LpMLDY7oPXFFOPe6sdjBFtvDVDBHwGqnDWltzlm8OXc2BhwoDJnvmwNWtOYm3nSrlUqHGFoWxI4s1xK4oOmQ5uAOZL3WfF9TxNt21iUtbmDd5f4N/xSdFUA7yI2NzH6h22Wee91YHmjeN9v/TDXgoodhLVOhLXb4uEzmKt5TiCnXji6ZLYl3qIPIsSbd7/L3XRc8vRxjMTfxttZayU5yzeV+RNgitRva2HKNGRwxY5l7r0OuGwNzGvBa7oDriHHd6KsV7wPacx1faEfo9n3nYs4Ljcz27/P3zv95jZgRGRvTmK6PKa5Zmq2Id2xUdKwg0dV+RnOfL/y2fPi+cJ53TGtwTuJtO+hcNyvZUrnHTBnZsk0VH3qa3Pei9HUP+ESp051v2wB/547P1MqYVvhqxZtLBOzLZ5cMWA7vz7/waQBsIEwLSbiMwQ4MDuiObnS/20XOBu12uZDbWHf4DCD6YANesus8V7zt8pGuZBi+wV0spS3vGGI7JHeO3D3/Evi8NnMSbzsdwXgDu0wvxe2qcm9jRTR18M34gxyhTLmuGxTqnu/GK4xtRKxWvEnoReWceNccCAvn5py/R7tiv9/nUAzsixpyo1DkY2DQxdPcs7UIbGBNSJzd54oldQ1m3zE0mCtVvBm0aOvNtgmb9nCoV2Js8bZu81CHdsCnHLosO6be7Pu8NnMS7x/n3K5lerFLj1TubThYSQ34oss8d9ov5bqn93Ue6O5jWKd9n9dm8+JtRcB9afhZl2UcWqhvNxbog/PdOSJqr8+dbBiscX1f1ydAuS+AHbkOOYY2uCFuczZ6urm4/IyJN4Z2YGOLNzukNSThmYt4u+3c7aDt5iFdfcfSGFu8abWmern6XOa1rztHNi/etqN1rRa7ttYlJB5WIPrgtXOCHKy1xR1vUirxC3nLHEpZ3kNHqkPE27ooKdwll+mNLd5rStM4F/G2npi+98S+g0PnxKdmTPGm0ZJjPAxxmQ+57hzZvHgD3XmJ7brAOYo38GnIORu98/6WyhDxtp3uC3mjcN/AhNbBK3BeidE/ByJLsfxCgz8buFVr2iWmT4id+rLznnOugzmUO+EUROrU1FCXee51p4LR630Hl709Auct5Xl/ETu/Rc5oGscd7U7YZQ7ibTuO1ArasngD7ZiBHEpMHQy1chjjsKSR9xymXVLF23ct68WZc3rTOZQ78PFo5LyzQ1zmQ647FbYNDjmW9MwtYjtK5sq+43fg2VzF23YcqW6knCj3OTFUvDnwyc2QFGN5/wTOG2KpMYfBnAWji1gL8Dtw3pAOKaZP6Nq3uYulbCwyh3LnYDO33ee6zIdedypiLe9n4LzFTufEvFh9I7ra4k33ba54W5FIHY3mup+WGm1uscl7crwWIWrPeS9VuGNgvU49521F2VfOSxHvELXLfaiAcjCV2mctVbhj2PycNxttlwVWW7x5fzkvDD0FHI3eE7+f8x1gPu63IeJ9R1u8S0ee1hTvNQs3MB/xBj7vVqzIL7kTrVnuJQQ0J0p8zcINSLxbk/4uY4h3TtQ3k8oc8WnUKS5wWvw5lb70aHMOenbIH/iEqCneT4SF+4JuV9k/Afyv8vGf7CdrmJN425iXPtejnbrqa4d/oH65/xl4lhC1yp3vWUhAfd7HHdKnB4de90/Ur7M/Ip+lj82Id5+7hZ93CahPgEuJNzOzxULLiyNQ23nQ/fuAv9EuMXjDJUe8Oejh+e7Ah2U71I1eS7zvCGftO6N/MPhvlPGa+I7/5j7cmzmJt7scswsKvM+d+xfql/vfgWcJUaPcY71E98A57K9ijZwS1/0b9evsr8jn6aOGeDNZUCjxTOnzOrEiejA/xh+y7tM7mo6XmXVsEgYmP+nKotZ1U3bvXx/sIHxiy72+mRjfNjjbwdzwiZL38cCyg9WAdjravkbBzR0eaMrOHYnbgQ9Fr4QLvYZ4UyS+0L/HMduc7xn+UfkYSm3xtlZczDXYzuygj/Ddi1l+tLVyt3ElMfty+8qPg+yY2KCS1517ndUQb9sn+jSi9HmdcG2gPU6Bz7n29+D8nVbPHu2t5e5oW0OpeYoZ5d6H/a2ul+s78LmF7qSlulp2+J3d6oHul9Cdn3efeR/4PJcaW4LGjuaXnqyl9tyrXV4Zu8b/+j6XGQyP+LTBUCbDpVCy3N2A0NDh81rYwVaonEtedwnUEG+rh762UPq8Xhhyf0Z3A7C7gZ3Q7vxO5u881xeS3xfeH+PG7ut07f13kbKhRtfuOEshNN/e1Yi5CUlfdPsx8HkOpXcVS4klWHpwTi3xZjvIjcFwNyXh4H4tlCz30BKnlLJn+48RqJLXXQK15rw5OA1pROnzFktMINJQmP98DXl95wwHcSUHBFthj6bclt6xDmVsa17lvjwOaOpsDZ6fRcPdzWq+PDcsey2qqIO1WFzPkw9aoqsdUVfE51G5wT+Qv2C5015LI9Xz1SekqrOVw2joGp3hCc18kDpaQdzYATsXHHK/23iQ0kvttkAojsEnAjbIUtTFBibnxpuozjbCEeHlQKkcKvymWDaMs+AKiyMaa8+Kuc8LZDu1sXZPWwsMlOxbOeCLquY8Z62gPtHGpiANRa73DWJVZxvigLIjNLk2hcU3ReMuPexD4p3PHfk59SUE40HPVGhOmV6UPm+V6kwIUQRa231wuU1sWtClL7kZEy59yp3/tIOmmHXPIp8n4oJOX/Cv4FGdCSGKEOqQaCn4Opq1bMgxNuzI72gEPDVA1QqBAqDqEhPFzXXMJbaXFUKIQcRsvWiTZ8iaiMPm07cHk7/ETG3ZpBdaijg9dJn7pjlVZ0KI6jAyNibZi6yJNE5oZ0N0jy+ELXHr8dCa7OmJGeiqzoQQVaFwx1rSFCJZE+kc0JS3K+bf8LtrGam+1CyJa4IWdSjmQ3UmhKjCGe2I2FgrkN+RNTEMbpoTG0OgCP95EOMyJ6ozIURRmPP7ht+bOoSsQHZesiaGc8BHwEPLk76Rv9RMlCPGZU5UZ0KIqhzRduWG1nrLmiiHzcTlizl4QhH+UxPrMieqMyFEdWyiFp+1cAl8LtKwEfy+IMAH6m9iJPykuMwB1ZkQYiS477XPsj5C1kRpYrZ5jN0iU9QjxWUOqM6EECPBxBLfnnOYD12Ug+Ltc5uvYd/2JcN9AVIyC6rOhBCjYDOBifFgvIGCAOcLvVLaIUwIMTvYQWkN93gwmYemIuaLjUvQAEsIMSp7NELR1/kwYC1kdV/f52idd5gdmjnPK/qXgdFl7lsmtkNT5jdIPKaALvOUQE3VmRCiCHY9sev643rjB/wdDTux1I5sq9jNKdyANHbuL4Q9HYxyDi3jE3WgRyoln7/qTAhRBDeb2vf7b1/vIyawRuKdxh7dqVCfaET7jrhdrCQE02Fd5jF1RVRnQohinNBYDzyOSOuQgEbALxnf2zJDy53u9zPkgh2bPfKWfKnOhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQuTzf1JZ8O9yuTagAAAAAElFTkSuQmCC\" alt=\"tan(x) = 1x + 2x^3/3! + 16x^5/5! + 272x^7/7! + ...\" style=\"width: 247.5px; height: 36px;\" width=\"247.5\" height=\"36\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.85px 7.8px; transform-origin: 117.85px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConstruct the nth layer of this triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.883px 7.8px; transform-origin: 152.883px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Use the boustrophedon (or ox-plowing) rule.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = SeidelEntringerArnold(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = 1;\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%%\r\nn = 3;\r\ny_correct = [1 1 0];\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%%\r\nn = 5;\r\ny_correct = [5 5 4 2 0];\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%%\r\nn = 8;\r\ny_correct = [0 61 122 178 224 256 272 272];\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%% \r\nn = 13;\r\ny_correct = [2702765 2702765 2652244 2551202 2401024 2204480 1965664 1689872 1383424 1053440 707584 353792 0];\r\nassert(isequal(SeidelEntringerArnold(n),y_correct))\r\n\r\n%%\r\nn = 10;\r\ny = SeidelEntringerArnold(n);\r\ns = sum(y); \r\nv = round(var(y));\r\nd = y([4 6 9]) - y([2 5 7]);\r\ns_correct = 50521;\r\nv_correct = 8277369;\r\nd_correct = [2709 1024 816];\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(v,v_correct) \u0026\u0026 isequal(d,d_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-07-07T19:46:14.000Z","updated_at":"2025-12-15T13:25:13.000Z","published_at":"2020-07-08T01:44:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSeveral problems in Cody ask us to construct part or all of triangles in which entries follow a pattern. Cody Problems\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/37\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e37\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/1463\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1463\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44037\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e44037\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44904\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e44904\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involve Pascal's triangle, which consists of the binomial coefficients, and Cody Problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/31/problems/1845\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1845\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e extends Pascal's triangle to a pyramid. Cody Problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45423-bernoulli-s-triangle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e45460\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves the Bernoulli triangle, which consists of partial sums of the binomial coefficients.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem deals with the Seidel-Entringer-Arnold triangle (also called the Euler-Bernoulli triangle and the secant-tangent triangle). The first eight layers are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[                         1\\n                      0      1\\n                  1      1      0\\n               0      1      2      2\\n           5      5      4      2      0\\n        0      5     10     14     16     16\\n    61    61     56     46     32     16      0\\n  0    61    122    178    224    256    272    272]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe name \\\"secant-tangent triangle\\\" arises because the sides contain the coefficients in the Taylor series for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sec(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sec(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"tan(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\tan(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sec(x) = 1 + 1x^2/2! + 5x^4/4! + 61x^6/6! + ...\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sec(x) = 1 + 1\\\\frac{x^2}{2!}+5\\\\frac{x^4}{4!}+61\\\\frac{x^6}{6!}+\\\\ldots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"tan(x) = 1x + 2x^3/3! + 16x^5/5! + 272x^7/7! + ...\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\tan(x) = 1x + 2\\\\frac{x^3}{3!}+16\\\\frac{x^5}{5!}+272\\\\frac{x^7}{7!}+\\\\ldots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConstruct the nth layer of this triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Use the boustrophedon (or ox-plowing) rule.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58872,"title":"Find the Points Tangent to a Circle from an External Point ","description":"From a point where do the lines touch a circle tangentially?. The loldrup solution may provide some guidance and alternate method. I will elaborate a more reference frame modification geometric solution utilizing Matlab specific functions, rotation matrix, and translation matrix.\r\nGiven point(px,py) and circle [cx,cy,R] return the circle points [x3 y3;x4 y4] where lines thru the point are tangential to the circle.  The line ([px,py],[x3,y3]) is tangential to circle [cx,cy,R] at circle point [x3,y3]. D\u003eR.\r\nThe below figure is created based upon h=P=distance([cx,cy],[px,py])/2=D/2, translating (cx,cy) to (0,0), and rotating (px,py) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,P]. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\r\nP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(h-Y)^2 = Y^2-h^2+2hY-Y^2=2hY-h^2 thus\r\nY=(R^2-P^2+h^2)/(2h) =(R^2-P^2+P^2)/(2P)=R^2/(2P)=R^2/D\r\nX=+/- (R^2-Y^2)^.5=+/- (R^2-(R^2/(2P))^2)^0.5=+/- R*(1-(R/D)^2)^0.5\r\nThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [cx cy]\r\n\r\n\r\nThis figure shows the point (px,py) rotated onto the Y-axis at position 2P. The circle (cx,cy) has been shifted to the origin with radius R. The green line shows a tangent at (x,y) from (px,py). A second tangent point is at (-x.y). D=2*P","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 952.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 476.25px; transform-origin: 407px 476.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 204px 8px; transform-origin: 204px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFrom a point where do the lines touch a circle tangentially?. The \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://math.stackexchange.com/questions/913239/given-circle-and-point-where-does-the-tangential-line-through-the-point-touch-t\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eloldrup\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e solution may provide some guidance and alternate method. I will elaborate a more reference frame modification geometric solution utilizing Matlab specific functions, rotation matrix, and translation matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven point(px,py) and circle [cx,cy,R] return the circle points [x3 y3;x4 y4] where lines thru the point are tangential to the circle.  The line ([px,py],[x3,y3]) is tangential to circle [cx,cy,R] at circle point [x3,y3]. D\u0026gt;R.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.5px 8px; transform-origin: 366.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe below figure is created based upon h=P=distance([cx,cy],[px,py])/2=D/2, translating (cx,cy) to (0,0), and rotating (px,py) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,P]. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 358px 8px; transform-origin: 358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(h-Y)^2 = Y^2-h^2+2hY-Y^2=2hY-h^2 thus\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188px 8px; transform-origin: 188px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eY=(R^2-P^2+h^2)/(2h) =(R^2-P^2+P^2)/(2P)=R^2/(2P)=R^2/D\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211px 8px; transform-origin: 211px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eX=+/- (R^2-Y^2)^.5=+/- (R^2-(R^2/(2P))^2)^0.5=+/- R*(1-(R/D)^2)^0.5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378px 8px; transform-origin: 378px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [cx cy]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 556.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 278.25px; text-align: left; transform-origin: 384px 278.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 419px;height: 551px\" 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\" data-image-state=\"image-loaded\" width=\"419\" height=\"551\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.5px 8px; transform-origin: 378.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis figure shows the point (px,py) rotated onto the Y-axis at position 2P. The circle (cx,cy) has been shifted to the origin with radius R. The green line shows a tangent at (x,y) from (px,py). A second tangent point is at (-x.y). D=2*P\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n%Find points on circle that when drawn to a point only touches circle at the circle point.\r\n%The line from the circle center to (x3 y3) is orthogonal to the line [(px,py) (x3,y3)]\r\n%A second point (x4,y4) also creates an orthogonal lines intersection\r\n\r\n  D=norm([px-cx py-cy])\r\n  \r\n  %Y=\r\n  %X=\r\n  \r\n  xy=[X Y;-X Y];\r\n \r\n %Rotation Angle: atan2\r\n theta=atan2(px-cx,py-cy); % (X,Y) output radians Neg Left of vert, Pos Right of Vert\r\n \r\n %Rotation Matrix: [cos(t) -sin(t);sin(t) cos(t)]\r\n %Translation matrix: [cx cy]\r\n %Check of (px,py) being regenerated from D, theta, and translation\r\n [pxyD]=[0 D]*[cos(theta) -sin(theta);sin(theta) cos(theta)]+[cx cy]\r\n [px py]\r\n \r\n %xy=\r\n \r\n \r\n  \r\nend %TangentPoints_onCircle","test_suite":"%%\r\nvalid=1;\r\npx=6;py=8;cx=0;cy=0;R=4;\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n\r\n%%\r\nvalid=1;\r\npx=-6;py=-8;cx=2;cy=4;R=6;\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n\r\n%%\r\nvalid=1;\r\npx=6;py=8;cx=1;cy=-2;R=5;\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n\r\n%%\r\nvalid=1;\r\n%px=6;py=8;cx=1;cy=-2;R=5;\r\ncx=-5*rand; cy=-5*rand; R=4+rand;\r\npx=3+2*rand; py=3+2*rand;\r\n[px py cx cy R]\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-12T23:33:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-12T21:15:25.000Z","updated_at":"2023-08-12T23:33:27.000Z","published_at":"2023-08-12T23:33:27.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFrom a point where do the lines touch a circle tangentially?. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://math.stackexchange.com/questions/913239/given-circle-and-point-where-does-the-tangential-line-through-the-point-touch-t\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eloldrup\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e solution may provide some guidance and alternate method. I will elaborate a more reference frame modification geometric solution utilizing Matlab specific functions, rotation matrix, and translation matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven point(px,py) and circle [cx,cy,R] return the circle points [x3 y3;x4 y4] where lines thru the point are tangential to the circle.  The line ([px,py],[x3,y3]) is tangential to circle [cx,cy,R] at circle point [x3,y3]. D\u0026gt;R.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe below figure is created based upon h=P=distance([cx,cy],[px,py])/2=D/2, translating (cx,cy) to (0,0), and rotating (px,py) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,P]. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(h-Y)^2 = Y^2-h^2+2hY-Y^2=2hY-h^2 thus\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eY=(R^2-P^2+h^2)/(2h) =(R^2-P^2+P^2)/(2P)=R^2/(2P)=R^2/D\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eX=+/- (R^2-Y^2)^.5=+/- (R^2-(R^2/(2P))^2)^0.5=+/- R*(1-(R/D)^2)^0.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [cx cy]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"551\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"419\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis figure shows the point (px,py) rotated onto the Y-axis at position 2P. The circle (cx,cy) has been shifted to the origin with radius R. The green line shows a tangent at (x,y) from (px,py). A second tangent point is at (-x.y). 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/Do4Lwc9YcXGxx+NRPYfSOIjc39XU1DRr1kwaab7uuuvCPdsaNyhN+xg0aJDymXzxxRcj7Egg9rgQvKelpaUR4kJw6FR58803fT5fRkaGqjAQUrhTFrOzs8eOHRvyLqr91SjZrQpJmpmrihfnz58PFxcCgUDTpk2FENdee+3kyZP37Nmj2qDqYA75vk7wQNV41EnCFaKUEn+s+F5xCyIuSJjqaGnShKwIFzhq1qxZs2bNhg4dWl1d/e9///vBBx/s27dv165d5ZmJqpmPiVxSZs6cOfK/L7jggvbt2yuXyPr16ydfoaWsrKx9+/aTJk264oorlJdt+frrr4UQzZs3V9338ssvF0KcOnUqQjN8Pl9lZWW4v4Z8xmrXrq1a0rJly2nTpp04cUK66fF4pkyZIl124l//+leER9eywWbNmjVt2nTOnDnPPPOMx+OZMWNGamqqfCkhLTvSp0+fcH/q3Lnz3XffHXJPf/GLXwghpG+6StLnXMhpm7J//OMfI0eOzMnJWbdunfKyDZGNHDlSnmPYoEGDevXqqabEKkV+4QxuVeRnWHqsX//618rlXq+3du3a4R508eLFvXr1WrNmzZo1a6THveWWW4YNGyYVNlTCva8TOVA1HnWSrVu3iqDOQSXxx4rjFYeVERdsprq6+vbbb2/cuPHf/vY35XKv1/vAAw9s2bJl7ty5q1evlidUmysjI2PRokVXXnnlwIEDc3Nz5YnWUmopLy9XrX/mzBkhRISPHOXdtfP7/aolX375pfhpfz1x4kTpH6NGjXr99dcT3ODtt9/+5z//efHixQUFBcuWLevbt2/InQq3I++++27wkyO57LLLwrVK+rApKytTLS8rK4v8UdevX78XX3yxVatWixYtUl4ZM6q8vDzV+QKRxfTCJbVVkZ/hBg0aCCFOnjyp/UGzs7M3bNiwf//+t99+e/Xq1YsXL37sscdWrFjxwQcfaN9IggeqxqNOCCGV/aqrqyO3J/HHSuT7CayG19LSpPh/+vRpeYnX6120aNHYsWOVC2XSR0LUj1sj5ebmjh8/XgjRp08fuc2NGzcWQuzevVu1sjQ9qn79+hE2+N1336m+9ikFP2PSXVRd/65du4QQV155pXTzpZdemjdv3uDBgwcOHDhv3rxXXnkl8k5F3WCfPn08Hs+cOXPmzZvn9/tvv/32mHbkwIEDlWE8/fTTEfa0VatWmzZtUn7q+P3+TZs2tWrVKty+3HTTTS+++GJRUdHatWtj+lSOVeQXzuBWRX6Gpcs6HT58WHmXU6dOfffddyG3Vl1dvXr16qNHj+bm5g4dOvTNN988efLk1VdfvWXLFul7vErI104kfKBqOeokzZo183g8ypNdJd26dZMjQuKPFdMrDusjLlia9LG6YcMG5cI77rijqqqqV69equ7m008/ffPNN+vVq6c8Wzpu0teCcN8//vSnPymvGB3Z3Xff3aZNm8OHD48aNUpakpub27Rp0zfeeEN5JYbDhw+/+eabWVlZ0tUXQjagvLy8qqpKGrMIKeQzJoR45plnVA9UUFAgzRU9ePDg0KFDc3Jyxo0b9+STT2ZnZ999993SbyJEEGGDQoj09PTCwsK33npr6dKlDRo0CD7xPeqORBVyT2+66aaqqirlEP60adOqq6tvuummkBv5+9//Pn/+/OLi4jfffFOa/pIkMe2vYa0KJyMjo02bNqrjUzqVIKT333+/U6dO8uEthEhLS5M+KaXBCNXBHO4oFYkdqFGPOpnP52vXrt3GjRv37t0rL1y8ePGCBQukaQ2JP1biRzgsx+zJE06j76SYVatWiaALOFZWVkrnJdatW7d3796TJk2aMGFCcXGxVLGUrxMX8qqOPp9P41THt99+WwiRl5c3ePDgzz77TEtrI1x3Yd++fVLNQ76S/Jo1a7xeb7169aZNm7Zy5crp06dLfaLc/pANkM75fu6556SbwVMdg58xaTeFECNHjly+fPmMGTOys7N9Pp98qqT0zVu+3t/KlSuFEAUFBcqbyknvUTeobL8QIuQkO9WOBGKf6hjy2Dhz5kxubm5qauqkSZNWrlw5adIkn8+Xm5srnWyi2p2vvvpKelEKCwuLg0S+vHGEKxyEpNzf4KdUychWRbB582av15uZmfniiy8uX7581KhR0mUVwk11lI4i6Qroy5cvl84Tlk8WUB3MIV+7BA9U5QMFH3XBz/mOHTtSU1OlN+Dy5csnT55ct27djIwMaXJ0Io8l0f6KWx9THSXEBZ3pe2BJV6cJnqv/7bffjhw5UvXThQUFBRs3bpTXSTAu1NTUyBMg3nzzTS2tjRAXAj9cn7hRo0byWWFr1qyRvmZJGjdurPyZqJANGDhwoMfjka80FRwXgp8x+YRS+co8eXl58hluUqvkOd6Svn37ih+uEhEuLoTboKolQogDBw4EPxuqHQnEHhfCHRuHDh1q06aN/Ky2adNGeVqKcnekKx2FE/ny4bF+MCv3N/KHh5GtimzVqlXy/NA6depI52iEiwtfffWV8tcpPR5P79695TM/VQdzyNcuwQNVfqCQR13I53zTpk3SCR2SVq1aSbk8wceSaH/FrY+4ICEu6Ez3A2v06NGqzxWlL7/8cuXKlatWrZK/Purr3LlzGi/vE7fS0tKVK1eGu0KlsgFS99SrVy/5ryF/M0L1jMndunTBKC3n46ksWbKka9eu8k3tG8zKygp54nvwjgTi+s2ICMeG9KyGvESPanfiJjTXJoP3V682GOCTTz7ZuHGjxmtinjt3btWqVevWrQtZBVEezMGvXeIHqiTcURfuOZcOlXA9THyPZetXPBhxQUJc0JnuB9aJEyfS0tJiOmvcqWbOnCmEkH9yMxAmLqiesVh/aitY7969lV+qNG5Q+m2nGTNmaNmRQFxxIb5jQ7U7cdMeF0K+cLq0wb6CX7vED9RAxKNO9+c8piPc1q84cUFCXNBZMg6sxx57LCMjI9nf8q2vadOmqivnSHHhqaeemjZtmvKbtPIZS7AXLi0tHTx4sOq6T5E3OGTIkIEDB9atWzc3Nzfkt1LVjqxZs2batGm9evWKNS4EYj82gncnbtrjgmp/dWyDraleuwQP1MhHnb7PeaxHuN1fceKChLigs2QcWNLl1UaPHq37lm1kxowZWVlZqotUSmd7S5S/Tax8xkpKSnw+X4Jf2pSiblA6Da9evXryvM7IO6Lci7fffjumxph4bGiMCyFfOASCXrsED9TIR52+Yj3C7Y64IEkJBAIRJhYhVvn5+dJvvevr+PHj+/bti+mSOA6zffv2tLS0yJcmVDLxGauqqtq+fXuLFi1CXqMm1h2Jyqw9TUnR1Hvovr9OouNrF/mo05fBR7jpktSr2w5xQWccWHAJjXEBsDt6dQmXaQIAAFEQFwAAQBTEhSikn1qWHT58eOXKlRSmAACuQlyI5Nlnn1X+8OPChQtvvvnmFStW3HXXXf/+979NbBgAAEbiB6xDO3ny5Lhx41asWPHzn/9cWlJTUzNmzJi5c+c2bNiwvLy8U6dOhYWF0g/dAgDgbMSF0CZNmpSenv7YY4/94x//kJa8++67devWbdiwoRAiPT29ffv2GzduDBkX8vPzgxcyfgHLSklJie+OhcdShBCLIv3eeFicVQELCtl7Q0JcCE26ovu6devkJRUVFY0aNZJv/vznPw+XAEgGsI64o0BkN5QmuoVwDSNGwEQhe28yhIS5C6EFX36kpqZG2cHVqlWLfg2WkhJKgtsMd303XRocUsi9SFLoAaAd1QWtfD6f3++Xb9bU1Ph8PhPbAyTyIarjR/4NpWJhZvxb07gXVCMAc1Fd0OrSSy/dtWuXfLOioqJ58+YmtgduE9MX7qiXf0+wMYnkA5UEW0gFAjAGcUGrli1bCiGk2QyfffbZxo0bCwoKzG4UnCymarxhgwUhSXMe9RVHjCA6AMnDYIRWHo/niSeeeOCBB3Jzc3ft2jVu3LiMjAyzGwVH0f4hZ4UK/KL6Okx4jEPwvod83lQLrfCMAbbGj8TojB8jQay0pAQLvk9TUlJUcUHHEYq42fTJhJXRq0sYjABMELlsbuSZCImwQj5Q0fK8cc4FEAcGIwDjRPhwsmwmsDXlsxruyZeX8xIAEVBdAJJLYyHB+IbpQllgSMaERx1FLTxQbwAioLoAJAWFBIuLUHig3gAEo7oA6MbZhQQtLF5gCCfcS0O9AZARF4BEaZy0aHzDjGHBCY9xIzcA4RAXgPi5uZAQjk0LDCrkBkCFuADELORnhhsKCeE4qcCgQm4AJMQFIAYhPyHcGREicEaBQYXcAJcjLgDRRS4nmNUqS3FwgUElcm4wpUmAATiREogk3NQE41sCq5EPA+VBwkmYcCqqC0AIlBMS5MjxiHAoNsANiAvATzA7IW7uGY8IKWSaJDTAMYgLgBCUE5LAVQUGJUIDHIm4ALejnKAjlxcYlMKFBnIDbIq4APeinJBsri0wyJjWAMcgLsCNwgUFs9rjJBQYgjGtAQ7AiZRwl5DjDqa0BC4kHWzBJ15yEML6qC7ALagoGEZZYGA8IhjTGmBHVBfgfFQUYEHBlQbpJgcnrInqApyMioIVUGCIgDkNsAviApyJoGAuJjzGJHguJKEBVkNcgNMQFCyIAoNGVBpgWcQFOAdBwVIoMMQn5PCEWY0BZEx1hEMEBwWzWgIkTjURkvMtYTqqC7A9VVGBioJ1cEZlgpjQAOugugAbo6IANwgEAlzZCaajugBbCjlNwazGQCMKDHFjQgNMR1yA/TCf0UaY8KgjxiZgIuIC7IRpCnZHgSFxnGwJUxAXYBuMPtgUBQbdcS1IGI+4ABugqOAkFBj0woQGGIm4AKujqOAAFBiShwkNMAZxAdZFUQHQiDIDko24AIuiqOBgjEckQ3CZwcTGwHmIC7AcigqOxHiEMRiYQJIQF2AtFBVcggJD8lBmQDIQF2AVFBUcjwKDkSgzQF/EBVgCQcGFKDAkG/MfoSPiAkwWXFQwsTFINgoMBmNgAnohLsBMFBUAAzAwgcQRF2AaigrupCwwMB5hGMoMSBBxASZgAAIwBWUGxI24AKMxAAElCgwGY/4j4kNcgKEoKkAw4dFsDEwgDsQFGIesgJAoMJiCgQnEhLgAIzBZASoUGKyAMgO0Iy4g6ZisgKgoMJiIxAAtiAtILooKCIcCg3WQGBAVcQFJRFYA7ILEgMiIC0gKJisgVoxHmE45VsjkR6gQF6A/JitAI8YjLIgyA0IiLkBnFBUQNwoMFkFiQDDiAvREVkCsKDBYE4kBKsQF6IPJCtAFBQbrIDFAibgAHTBZAYmgwGBZJAbIiAtIFEUFwMFIDJAQF5AQsgJ0oSwwMB5hNZxgCUFcQCLICoB7UGZwOeIC4kRWQPJQYLAmEoObERcQD7ICdMeER1sgMbgWcQExIyvAABQYLIvE4E7EBcSGrIDkocBgFyQGFyIuIAZkBRiJAoOVkRjchrgArcgKMAAFBhshMbgKcQGakBUABCMxuAdxAdGRFWAWxiOsj8TgEsQFREFWgMEYj7AdEoMbEBcQCVkBpqPAYAskBscjLiAssgLMQoHBjkgMzkZcQGhkBVgHBQa7IDE4GHEBIZAVYDoKDDZFYnAq4gLUyAoAEkFicCTiAn6CrADrUBYYGI+wF3oP5yEu4EdkBQB6kfsQCgzOQFzA98gKsDgKDLZDYnAS4gLUyAqwDiY82h2JwTGICxBC8U4mK8DKKDDYEYnBGYgLICvA0igwOACJwQGIC27HuxeAkehzbIq44GpMb4QtcEalA3AxBrsjLkAIsgKA5CMx2Bpxwb2YsgCbosBgXyQG+yIuuBRZAfbChEfHoM+xKeKCGxHqYXcUGGyNEyXsiLjgOkxvhE1RYHASEoPtEBfchawAx6DA4BgkBlsgLrgUWQF2RIHBSeiF7IW44CJMbwRgKQxJ2AhxITb//e9/V65cuXv3brMbEjOyApyH8QgHIDHYBXEhBi+88MKtt966YsWKP//5zw899JDZzYkB70M4BuMRDkZPZWVesxtgG36/f+LEiQsWLGjYsOGpU6cKCgpuueWWxo0bm92u6JjeCAcrPJZCgLC7QCBAULA+4kIM/H5/amqqEOLCCy9MSUmpqqoKuVp+fr5qyb59+5LeuDDICnCehZkBhiEcRk4MKSkp5vZUwR04JMQFrTwez5gxYwYPHty5c+eNGzcWFxc3a9Ys5JomhoMIyApwKgoMzmCRxBDcgRMgJMxdiMHWrVsvvPDCSy65pG7dup9//vl3331ndouiYHojnIp84GyMTVgQcUGrVatWffTRR7Nnzy4pKZk6daoQYvr06WY3KhLebwDshS82VkZc0KqioiI/P79WrVrSzZycnMOHD5vbJI14B8KRlAUGpjI4BudVWhZxQavLL798w4YNn3/+uRDi1KlTW7dubdWqldmNCothCAA2RWKwJqY6atW4ceORI0f27NmzSZMmu3bt6tGjx0033WR2o0LjPQYXYsKjI5l+ogRkvBI6y8/PN/3MCEoLMIBF+nHlMARxwUms049ZoVe3AgYjxE4UlwAAIABJREFUnMY67zHAYMxgcBKGJKyGuOAovK/gNlQUHIzEYCnEBWeitAB3osDgVCQG0xEXnINhCLgTBQYHozezDuKCQxC9ATgSQxIWQVxwGsI4XI7xCCAZiAtOwDAEXI7xCGejwGAFxAXb4/0DqFBgcDB6PLMQF5yD0gLcjAKDs9G/mY64YG8MQwAhUWBwHoYkzEVcsDHeM4ASBQYgeYgLTkBpAYAbUGAwEXHBrhiGAIIpCwyMRzgSicEsxAVb4n0CADASccHeKC0AEVBgcCQKDKYgLtgPwxBABEx4BJKBuADAySgwOBIFBuMRF2yG0gIQFQUGNyAxGIy4AMDhKDAAiSMu2AmlBUAjCgxuQIHBSMQFAIDtkRiSjbhgG5QWgLgxHuFU9IeGIS4AcCbGI1yCIQljEBfsgdICkCAKDEAiiAsAHIsCg0tQYDAAccEGKC0AuqDAAMSNuGB1ZAUgERQYXIICQ7IRFwAAQBTEBUujtAAkTllgYDzCwSgwJBVxAQAAREFcsC5KC0AyUGBwMAoMyUNcAOB8THgEEkRcsChKC0DyUGBwMAoMSUJcAOAKFBiARBAXrIjSAgDEjQJDMhAXALgFZ1QCcSMuWA6lBQBIEP2n7ogLAFyKAoMbMB6hF+KCtVBaAJKKCY9AfIgLANyLAoODMeFRX8QFAO5CgQGIA3HBQhiJAIxHgcHBKDDoiLgAwHUoMACxIi5YBaUFANAdBQa9EBcAuB3jEUBUxAVrobQAGIPxCPegwKAL4oIlcBAD5qLAAERGXADgUhQY3IPCbeKIC+ZjkiNgBRQY3IBSbtyICwDciwIDoBFxwSooLQBA8jDhMUHEBZNx4ALmUhYYGI8AwiEuAACAKIgLZmKSI2A1FBgcjPGIRBAXALgdEx6BqIgLpqG0AFgTBQYHo7+NG3EBACgwuA7jEbEiLgCAGgUGQIW4YA5GIgCrocDgEvS68SEuAADciPGImBAXzETIBSyL8QhAibhgAiItYE2MR7gEF2CIA3EBAEKjwADIiAsA8CMKDEBIxAWjcU4EYCMUGJyK8YhYERcA4CcoMADBiAsAADeixBsT4oI5OEwBK1MWGBiPcDzGI7QgLhiKgxIAYEfEBQCIggKDU1Ho1Y64YAIOUMD6mPDoKpR+oyIuGIfDEbAvCgxwOeICAIRGgQGQERcAQBMKDI7E6LBGxAWDcDFHwI4oMLgH48WRERcAAEAUxAUA0IrxCLgWccFQjEQAtsN4hOPRM2tBXDACQ2KAY1BgcDD66giICwAQBQUGgLhgHOpdgDNQYIALEReSjuoW4AAUGJyNr3NRERcAAPgeX/DCIS4AgCbKAgPjEXAb4oJBqHQBAOyLuJBc1LUAp6LA4DB8qYuMuAAAWjHh0Q34mhcScQEA4kSBAe5BXIhNeXn5qlWr3n//fbMbAsAcFBjgTl6zG2An69atGz58eJs2bQ4cOHDBBRfMmDHD49GUtxgSAwDrCwQCjESEQ3VBq5qamuHDh0+aNGnChAnz5s2rqKhYvny52Y0CYALOqHQ8QkMwqgtarV27Nisrq1WrVtLNJUuWRL0LBxwAwBmIC1pVVFRkZ2ePGjXqrbfe8nq9gwcPHjBgQMg18/PzDW4bABMVHkthQoPz0JOrMBih1WeffbZixYomTZrs3Llz9uzZzz///Pr160Ouue8HBrcQgGHIB04lTzWjJ1chLmiVk5Pzv//7v8XFxUKI/Pz8zp07L126VMsdmecIOB4zGOB4xAWt/ud//kd5s1atWrVq1TKrMQBMR4HB2Zh8pkJc0Kpjx44nT55cs2aNEKK8vPzdd9/t2rVrhPU51ABXocAAZyMuaPWzn/1s8uTJjzzyyM0339ylS5ebb765devWZjcKgJkoMMA9ODMiBi1atJCqCwAAuArVheRiniPgHoxHOAP9dkjEBQCIH+MRcAniQlIwzxFwJwoMTkJPrkRcAICEUGCAGxAXAEBPFBjgSMQFAEgUBQY4HnEhiZheCwBwBuKC/pgdA7iQssDAeITd8WUvGHEBAABEQVwAAP1RYHAGqsUy4gIA6IMJj3Aw4gIAJAUFBjgJcQEAdEOBAU5FXEgWJtYCoMBgX/ThKsQFANATBQY4EnEBAICwPv30U7ObYAnEBQBIIsYj4AzEBZ2RQwEwHgHnIS4AQHJRYIADEBcAQH8UGOAwxAUASDoKDLA74gIAJAUFBjgJcQEAAERBXACAZFEWGBiPsB0u7KjkNbsBzsRBFp+77747LS1t3LhxquVHjx7dsmXLd999V7t27Y4dO9apU0fjBhcvXlxdXR283Ov1+ny+1q1bB2/q2LFj999/f2Fh4S233BLHLoSj766VlZVt3LhRCHH99df7fL7IKydpjwC4SwC64lmN26OPPiqEmDt3rnLhN998U1JSojxivV7vsGHDampqtGwzLS0t8vHftGlT1SMGAoHu3bv7fL49e/ZYdtdWrlwp3eXrr7/W0gDd9ygQCHCca3RDqVD+Z3ZzEBu6dBnPgs44tuKzZ88ej8fTqlUr5cJz585dffXVQgiPx1NUVNS/f/82bdpIz3D37t21bFaKCx6PxxdE+Tn92GOPKe/12WefBTfGUrsWa1zQd48kHOfaERfsiy5dxrOgM46t+HTp0kUIsW7dOuXCUaNGCSHS0tI2bdokL5w+fbr0JM+cOTPqZqW40Lt37+A/1dTUzJw5MyMjQ/rMVn3zHjhwoBBi+vTp8e7Qj5Kxa7HGhYCueyThONeOAoN90aXLeBb0JH9bNbshNrN+/XohRLNmzZQLz58/L33Yjx8/XrV+//79pXGEqFuOEBck8ufuPffco1y+b98+IUR2drbGUY9wkrRrccQFvfZIxnEeE+KCTdGlyzgzAuYbM2aMEGLQoEHKhYsXLz59+rQQol+/fqr177jjDiHEzp079+7dm+BDd+7cOTs7WwjxxRdfKJfn5eV16NDh8OHDL7zwQiLbN2bXqqurV69evXTp0vfffz/cOnrtERLHKRKwI86MgMn279+/atUqj8fTs2dP5fI1a9YIIXJyctLT01V3adGihdfrra6ufv/99xs1apRgA3Jzcw8fPlxVVaVaXlxcvG7duilTpgwYMEBasnr16lmzZkXd4H333dekSRNh1K49/PDDTzzxxNmzZ6WbmZmZ//znP/v06RO8ZvAewTALMwOkBPtKSUkJuP58N+ICTPbqq68KIdq0aXPxxRcrlx86dEgI8dvf/jb4Lh6P51e/+tX+/fs3bNhw++23J/Lofr9/06ZNQojgcyi6du06ePDgjz76aO/evdIn9549e+TpBRF0795digsG7Fq3bt3Wr1+flpbWtWvXM2fOrFmz5tixY7fddpvX6w0+bTJ4jwBAI+ICTLZs2TIhhHSagNJ3330nhPjFL34R8l55eXn79++X1knExIkTpe/l7du3V/0pOzu7Xr16x48ff/vtt6UP1/z8/N69e0fd5mWXXSb9w4BdW79+/bBhwx599FHpXI+DBw+2a9fu8OHDo0ePDo4LwXsEsxQeS+ES0bAX4gLM5Pf7t2zZIkJ9pm7btk0I4fWGPkSl5efOndPyKNXV1dJcAdn+/fsPHDgwb968mTNnCiGysrKkOYYqBQUFCxYs2Lx5s3Szc+fOnTt31vKIwqhd6969u/LSTzk5OSNGjBg8ePD+/furqqqCr+Ck2iMYifEI2BpxAWbavXu33+8XQlxyySWqP0nLw/F4PFHXkc2ePXv27Nnh/lq3bt358+eHvKCTNLfg448/1vIoKsbsmupCT0KI3/zmN3IDmjVrpvprInsEfVFggL1wZgTMJJ+P8P/+3/9T/Sk1NTXCHaVPU+mTNT4ej6dRo0YPPvjg7t27W7ZsGXIdqVWqkyY0MmbX6tevH27jp06dCl4/kT1C4sgHsC+qCzCTPJ9fNRlQCHHFFVccPXo0+IQFibT8wgsv1PIovXr1mjp1qnKJx+NJTU2N+pEsTS+QG7ls2bLnn38+6sONHDmyRYsWxuxaw4YNtawmU+0RzEWBATZCXIBFSaMDlZWVIf+6Z88e8UNpPSqv1xv1xyNCkvKEnCo+//zzBQsWRL2XdP3ECHTctVip9gjGYwYDbIq4ADPVrl1b+kdlZaXqAzI/P18I8emnnwbfy+/3Hz58WAjRqlWrpDbv5MmTQlHev/baaydPnhz1XldccYWw6q6p9ggANCIuwEy//vWvpX9s27ZNddJB27ZthRB79+4tLy9Xfdxu2LBBGuC/6qqrkto8aUqg3MjGjRs3btxY432tuWuqPYIplAUGxiNgF9QkYaZGjRpJhfGvv/5a9afrrrsuPT3d7/cHTxeQJiI0a9Ys2RcPKC8vF6HmKmphzV1LZI8AuBlxAWbyeDwFBQVCiHXr1gX/6Z577hFCjBo1Sjlj4F//+pd0sYTRo0cr13/mmWe6devWrVs3HefxST8Q1a5duzjua81dS2SPkCRMZYAtMBgBk3Xp0mXjxo0hfxvpoYceeuedd9avX9+tW7d27dr96le/2rFjx86dO4UQ/fv3LyoqUq68bds26aO3urpal4Z9+umn0nfxP/zhD/FtwWq7lvgeyaa2yJL+f8fWowluyp2Y8AjboboAk0nXKt6+ffuxY8dUf/J4PCtWrLjnnnu8Xu/69etnzJixc+fOtLS0Rx999D//+U+yG7ZkyRIhRKtWreIe6bfariW+R1NbZEn/Hfvw6BgROPbh0bF85OmB6ADr41e29JSS8v17nmc1Jp07d161atWECRMeeOCBkCtUV1e/8847VVVVdevWbdu2bbjzABcvXnzDDTecP38+3PWVY9K6devNmze//PLLIX/dUSNL7VoieySVE2THPvyxqJDZnBpDnJQpgQmP1kSvLiMu6IkDKz7vvvtuhw4dmjRpkuDFiR955JHJkyd/9dVXiTdp9+7dV1xxRXZ29oEDBxK5SoF1di2+PVKlBMkdW39SVMhsniUtjLttrkVcsD56dRmDETBf+/bt27Vrt2vXrtWrV8e9kYULFz7xxBN//vOfdWnSpEmThBAPP/xwglc0ss6uxbpH0qCDauEdW4+GiwUhgwUiU0YExiNgcVQX9EQOjdvOnTuvvPLKVq1ahZwYqMWyZcs++uijv/3tb4k35uDBg7/+9a+bNGmyY8eOxLdmhV2LaY/CVRSUN4OrCyFXQ1QUGCyOXl1GXNATB1Yi/vrXv44fP/6tt94qLCw0tyW33HLL3Llzd+zY0aRJE102aPquadkjLSlBpowLowM/uS+JISaqogKJwWro1WUMRsAqHn/88UGDBm3cuNHcZhw7dszv90+fPl2vrCDM3rWoexTruEMw5ZqMSsSEfAC7oLqgJ3IobCSmcoKKqroQvEFqDNpRYLAyenUZ1QXAdRIvJ4REjSE+5APYAtUFPZFDYXGJVBSUQlYXgh+FGoNGFBgsi15dRlzQEwcWrEmvlCCLHBcEAxOx4xQJa6JXlzEYAThZksYdomJgAnAYqgt6IofCInQvJ6hErS4EN4MaQ1QUGCyIXl1GdQFwFLPKCSFRYwAcg+qCnsihMEuyywkqGqsLEmoMGjHh0YLo1WVUFwB7s1Q5ISRqDBqRD2BlxAXArqwfFGQkhjjwo1PWQWlBMBihO6lyxbOK5DF43CGkmAYjZIxKaMGER0uhS5dRXQBsw0blhJCoMQD2RXVBZ0RR6M4K5QSV+KoLEmoMUVFgsA66dBnVhaSQJ9MCibB7OSEkagyAHVFd0Bln3UAXFqwoKCVSXZDx0xLhcEaldVBdkBEXdEZcQCIsnhJkusQFwcBEeIxHWAH9uRKDEYAlOHLcISoGJrTgjEpYAdUFnZFGERO7lBNU9KouSKgxhESBwXT050pUFwBzuLOcEBI1hqgoMMB0VBd0lp+f/+mnnwrSKMILmRJMaUnc9K0uSKgxBKPAYC6qC0pesxsAuIVNxx0Mc8fWo/JTNLVFFs8MLCIvL8/sJlgCgxFA0jHuoBGjEhEwHgFzUV1IlpQUBnrcjnJCHKgxKC3MDJASzMLV9lSoLgD6o5yQCGoM4RAdYCKqC4BuKCfohRqDjAIDLILqAqADygm6o8YQEtEBZiEuAAkhKCQPiUHCKZSwAgYjgHgw7mAM6SmVnm2Xj0rAFIFAID8/3+xWWALVBf1xQoSzUU4wnvzchnzy3UBZYGA8AqagugBoQjnBXEx+BMxFdQGIgnKCRTCVQUaBIdm46EIw4kISccDZHUHBatycGJjwCHMxGAGoMe5gZYxKSAqPpRAgYCSqC8CPKCfYgmtrDOQDmIjqgossXry4uro6eLnX6/X5fK1bt65Tp47xrbICygm2Q41BUGCAsYgLSREIBCw4caFXr16nT5+OsELTpk1HjhzZs2dPw5pkOoKCfbkzMXBNaCNxVrwSccF1PB6P16t+3auqqoQQO3fuLC4u3r9//9/+9jczmmYcUoIzuDMxAKZg7kJyWbDGUFJSci5ITU3NzJkzMzIyhBCjRo3au3ev2c1MFmYnOIxr5zFIqDQkgwX7bSsgLkAIITwezy233DJr1iwhhN/vnzJlitkt0h9BwanclhiYrwBTMBgRj+3bt2dlZUnfxZ2kc+fO2dnZhw8f/uKLL8xui24Yd3ADN49KMOERxqC6ELPPPvvs1ltv3b59e+TVbDpHJjc3V/wwlcHuKCe4ivKVdXyNgXwA41FdiM358+cfeOCBmOoKKSkpdokOfr9/06ZNQoi0tDSz2xI/ygluJpcZpP+75HWnwJAMdum3DUN1ITYTJ07s3Llzw4YNzW5IUkycOPHs2bNCiPbt25vdlnhQTkhcSoqm/+K4i2Gzx1wylYF8kCTMcwyH6kIMNm/e/MEHH8yfP/+OO+6IsFrwj6Pn5+fv27cvmU2LQXV1terqC/v37z9w4MC8efNmzpwphMjKyurfv79JrYsTFQUtTO8GwzVA929xbp7KgEQoe+/gntzlbFMnN92pU6d69uw5ZcqUBg0a3HHHHX/6059+//vfB6+mTAZySrXIk3zRRRdFvkyTEKJu3brLly9v2bKlMU1KECkhsuTlgzFh/q2vBN83ysPDqUeF8kRK6g26CO63LfV9z0QMRmg1fvz4yy+//NChQ+vWrTtx4sTu3bujHkAWSQlaeDyeRo0aPfjgg7t377ZFVmDcIVjcxf9AIOb/Erl73HsUK5eMSiAZbNR7G4bBCK0yMjK++uorqVx/9OjRdevWXXTRRRqrVZaa7dirV6+pU6cql3g8ntTUVI/HBtmRcoJSTJ+gljkAI7Uk8h6p/qplj1w1KsGEx8QxcSEC4oJW9957r/zvCIMR1uf1eu144gNBQcSSD6wTDmISstnh9lq5PML+Ojsx8BMSMAxxAVYXctDBlJaYJWpKsGk40Ei1dyGfjciFB2cnBiUKDEge4kI8VMX8CKz505S24PJyQuSjxtn5IDLlvmsvPDg4MVBg0J11xo4thbgAy3FzUIiQEujBgsUUHQIBxyYGJQoMceOrXWTEBYNYarajNbk2JVBI0EXUMYuUFCHE0eebOzAxUGCAAYgLMJ87gwKFhKSSn0PV83znh85MDECyERdgGlKCCikhGYJzw50fHhVCSKFhaousOz886rBnnvGIRFAGDoe4kHTWme1YWVlpdhO+R1CQ0TUZRpUb5DLD882zprb4PkPY9+VgPALJRlwwDtMXhCuDAinBahS54ceBieebZ9354VHFvEgzWqYfCgyxssiXOisjLsAILkwJgqBgeYGAEOLH0yWkxCD9W3rt7PViUWBAUtngur+wNRf+uEPI3ziI4xcTYAzloSgXGyRG/u627ogO0BfVBSNYZ/qCYSgnyIgI1qe8iNPzzbPu2HpU+VLaqNJAgSFBjBdHQFwwlBumL7gwKJASHEB12cdA4Kj46Stro9CAWLnt61x8GIyAblw77qDCoINNBf/gdfBLGfevaRtGOcORSgN0RHXBIA4ej3BhOUGEqigQERwg5E9LSK+s6hWn2AC3obpgNCeFBheWE0SoigLlBCcJrjFIQk5WtXilQVBgiIXjR4oTRHUBMXNnOUFQUXCNyD9fGVxssFqlgQmPMXHSV7ikorqAGLiznCCoKLhPuBqDzEaVBqIDdEF1wTjy9AXbnR/h2nKCoKLgYpFrDBLLVhooMMTKXn2yKYgLiISgoER/4jbSoS69CyL8fKVlQwOiYiRCOwYjEJprxx0EQw/4KfmYD/mmkIUcnjARZ1RCX1QXDGX98Qg3lxMEFQWEoWVgQqKqNFBmsAVr9sZWQ3UB33NzOUFCRQERRJ38qKQ6eKwwC5ICQzBGImJCdcHtXF5OkAQHBSCY9hqDJBAweUIDEx6hI6oLRrNO1YtygkTZoVNRQGQx1RiExSY0EB1Csk6fbHHEBdOYWAcjKEhUJWI6DWgRa2IQpo5NKCc8QomRiFgxGOEijDsoERQQt1hHJSRWmAVZeCyFAIH4UF0wgfG1L8oJShQVkLg4agwS48cmyAfB5NICIxHaUV0wU7JPp6ScoMKURugovhqDsEaZAYgV1QVnopwQjKwA3cVdYxChJjQYgwmPiA/VBXPI12vSF+WEkAgKSJ64awwS5cmWySszcEalEiMR8SEumEyv8QiCQjhkBSSbxp+WCCf48gzJPkqZ8Ig4EBdsj6AQDkEBRpLLDNL/Y3oPBs9m0P1wpcCABBEXTJPgeAQpITKyAoxni4EJiWsLDIxExI2pjuaLNTQwjTEqLtQIsyQy+VEkef6jO/MB9EJ1wTYoJ2hBUQGmS7DGIILKDBzGsAKqC2aSq2GRCwyUEzSiqACLSLDGIIS6xqBXmUFZYHDhVAZGIhJBdcHSqCho57wLNZaVlW3cuFEIcf311/t8vvg2snbt2oqKCiFEQUFBvXr1Iqx5/PjxTZs2CSHq16/fsmXL+B4OMl1qDCLJ8x8B7YgLJpMnPCrPqCQlxMp5WUEIsWPHjm7dugkhvv766/T09Pg2cuTIkd69ewshrr/++iVLlkRYs1+/fkuXLvV4PFJGQeISTwwiyfMf3TnhkdJCfBiMsBbGHeLgyKygl1tvvbWoqEgIsXTp0ldffTXcaq+88srSpUuFECNHjmzdurVx7XO6xEclhN4/M+HCfCDhJygTRFwwnxR1n29eX9WbSCmBoBABPxalxdSpU6XixNChQ48fPx68QllZ2b333iuEaNas2ZgxYwxunuPplRiSdMaEC2cwID7EBSsiJWjBxEaNMjIynn32WSFERUXFkCFDglcYNGhQRUWFz+ebO3eux0OfoD9dEoMImv8YNxcWGJjkmDi6Bqu488PSOz8sJSho5MKiQnV19erVq5cuXfr+++/Het+ePXt2795dCDFv3rz58+cr//Taa69JSyZMmJCXl6dXa6FitcSgRIEBWhAXLEHjGZWQuDArPPzwwxdddFGnTp3++Mc/FhQU1K9f/5VXXolpC88991xGRoYQYtCgQSdPnpQWlpeXS/WGTp06DR06VPdmQ8lSicFVBQZKC7ogLsBO3DlZoVu3bo8++qjX6+3atWunTp08Hs+xY8duu+22WbNmad9IRkbG5MmThRBlZWV/+ctfpIX33ntvWVlZ3bp1X3755aQ0HT+lLB+anhiAmBAXrIICQ1Sunaywfv36YcOGlZeXL1q06J133vniiy+ys7OFEKNHj45pOz179uzRo4cQYvr06Vu3bl27du3MmTOFEFOmTMnKiv+jC7FSJgZdJj8mfh0nB49HUFrQC3EB9uDCooKse/fu48aNk6/UlJOTM2LECCHE/v37q6qqYtqUPCQxcODAu+66SwhRXFx88803691kRGGFgQlXjUcgccQFCyH8huPmrCCEKCkpUS35zW9+I/1j9+7dMW0qPT39ueeeE0Js37597969mZmZzzzzjC6NRKyskBiUHFxgEPSueuCqjlakvMIjXJ4VhBD169dXLUlNTZX+cerUKSFEdXX1e++9F3zH3/3ud16v+j3evXv3Hj16zJs3Twjx0ksvxX29SCROl8s+igR+kmphZsDZKYGxXR0RF2BpZAUhRMOGDSOvcPbs2Q4dOgQvr6ysTEtLC17+hz/8QYoL11xzjR4NRPxMTwxK7rwmNDRiMMJamPCoRFaAG5g7KuHgfMAkR31RXYBFkRW0S01NXblyZcjlxjcGcbBUjQEIibhgOSF/o9JtyAox8Xq9nTt3NrsVSIiOiUH88A7SmBiUMxgcMx5BaUF3DEbAcsgKcCe9RiWE+MklGQBdEBesyM1xmKwAN7NCYnDAuRKUFpKBuGBpbpvwSFYAdEwMsqgdiTMGIJBUxAVYBVkBkJh+BSdbFxgoLSSJeyfTJUl+fv6+fft02ZSrDnqygr2MVbxeo3m9kkbOCon8rr32N5cyJdi33qB7z6ljr25rVBdswPFDEmQFICS9foxKpr0vsWmBwVXfsgxGXLAulxzuZAUgAl0GJjQmBvtWFGAA4oKlOf4ij2QFICojE4MzuOS7lsGICzANWQHQyJTEYLvxCKd+rbII4oLVObXAQFYAYmJMYrDveITDekgLIi7ABGQFIA7G1xhsV2AQjEQkDXHBBpxaYBBkBSBGBiQGOxYYOCHCAMQFGE3unnhfA3HQPTFEZscCA5KBuGAPjikwkBWAxOmbGOxeYKC0YAzigv3YNzHYtuGA5SQ7MQAqxAXbsHtwZnojoC99f4xKlRiUBQYrj0dQWjAMccFO7DskQVYAkiHxxGDryzeRFYxEXICheFMD+rpj61HlT0vEsQUt70orFxhgDOKCzdixwMD0RiDZEvwxqpCTGCw+4ZHSgsGIC0gusgJgjAQHJqJOe6TA4HLEBfuxUYHB8g0EHEWvyY/yO9eyBQZKC8YjLiBZmN4IGC+RxGCX9ylZwRTEBVuyUYFB2KcPApxBl8QQssDAeISbERfsyuKJgSkLgIn0TQyWQmnBLMQF6I+sAJhOl3kMwYmBAoNrERdszOIFBgDmijsxqIK+dSY8UlowEXEJHzEVAAAgAElEQVTBIayTGCgtANaReGKwToHBOr2cOxEX7M1qEZusAFiNLonBOgUGYb1+zyWIC7bHkASAyBKfx6DqXYwvMDAMYTrigqOYmxgoLQCWFd9PSyjfy5YqMMB4xAUnsELcJisA1hfHT0tY4bxKSgtWQFxwCHOHJBgGAewijoGJkJ/Rho1HMMxqEcQFBzLx3UX0B6wv7qkMi+ob/Q5X9maUFsxFXHAOs95LDEMAthNrYjC3wCDIChZAXHAU44ckKBPCwVasWLFgwYIFCxacPn06wmo7d+6UVjt16pRhbUtcfDUGIwsMTFmwFOKC05g1iYG3M5zn0KFD3bp169at23333RdunYMHD3bo0KFbt24zZ86sU6eOkc1LXEyJweACA1MWrIa4gPgxDAFnGzBgQFFRkRBi+vTpCxcuDF6hqqqqsLCwoqKiQYMG06dPN7yBOogjMRg8g4HSgkUQFxzImAID0R9u8J///CczM1MIMWDAgOPHj6v+OmTIkJ07d3o8nlmzZtmutCDT5ceo9MUwhAURF5zJyCEJ3s5wsPT09FmzZgkhysrKSkpKlH+aNWvWtGnThBATJkxo3bq1Oe3TifbEEFxg0H08gqxgTcSF2Hz22WcrV6786KOPzG5IDJKRGBiGgHtcc801Dz74oBBi1apV//73v6WFn3766Z133imEKCwsvP/++81sn04sUmNgyoJlpRDftHv00UfXrFnTvHnzffv2paWlvfjiixdccIFqnfz8/H379pnSvGDJC+nEBZcbq+jSR7vgGPD7/c2bN9++fbvP59u2bVtubu5vf/vb3bt3Z2dn79ix4+KLLza7gbpRBgVlgFBJSRE3lP7kc12vS0RbsLRgqV7dRFQXtNq9e/fcuXPfeOONJ554YuHChZWVlYsWLTK7UVEkaUiCrAC38Xg8c+fOrV27dlVVVUlJyciRI3fv3u3xeF577TUnZQWhucYQCCRlwqMFswJkXrMbYBt169adOnWq3DU0aNCgtLQ05Jr5+fmqJVZIpikpVJKA+OXl5T355JODBg3avn379u3bhRDjx4+3+5SFkKTEIGWFqS2yItQYlAqPpSRYYLBIVgjuwCHhIyQeBw4c6Nq162uvvda4cWPVnyxYttL3TUhpAcJ9gxGyG2+8UTqjskOHDmvXrjW7OckVdWBCNSSRSFyw8sWeLdirm4LBiJgdP368b9++gwcPDs4K1mTur08BjuH3++VzKXfv3h18XqXDRB2YUH2s63KKhNWyAmTEhdjs3LmzqKiod+/egwcPNrst8UgwMVBagJv95S9/2bx5s8fjEUKUlZX16dPH7BYlXdTEoMsMBosMQyAy4kIM3nvvvf79+48ZM6Zfv35mtyU2yjdh3ImBrAA3W7p06ZNPPimEGDFixD333COEWLFixcSJE81uV9JFTgyJ9wZUPe2CuQtaHT58+MYbb5w4cWLbtm2lJR6Pp1atWqrVrDzKleDoIHEBMrfNXTh69OiVV15ZXl7euHHjbdu2VVdXX3nllfv37/f5fFu2bGnatKnZDUy6CPMYVGMQMc1gsPKUBZmVe3UjUV3QaubMmd9+++2gQYOa/OCxxx4zu1GxSeTdSFaAm/Xq1au8vNzn873++us+n6927dqzZ8/2eDxVVVXFxcVnz541u4FJF6HGoMsVFyybFSAjLmg1fPjwfT/18MMPm92omDHtEYjVmDFj1q9fL4SYNGmSPMG5RYsWY8eOFULs3bt3yJAhZrbPKBovyaB9wiNTFuyFuOA6cSQGSgtwrbVr10qxoLCw8K677lL+6aGHHiooKBDhf6/SecIlhjgKDHxjsR3igqvxjgUiKCsr69mzpxAiMzPzhRdeCF5h7ty5aWlpQojbbrvN8edVSrTUGKIWGGwxZQEqxAU3iulECUoLcK1evXqVlZUJIV599dX09PTgFbKzs5955hkhREVFRXFxsdHtM0nIxKC9wEBWsCnigkvpcmol4GCPPPLIqlWrhBAjRozo2LFjuNX69OnTo0cPIcS6dev++c9/Gtc+U8X985VkBfviREqd2euUm6hvXUoLCMltJ1IipOCzK5XDECHrDXac3mivXj15qC64mo3esQCs5o6tR+Uyg5Yagx2zAmTEBbeLcKIEpQUAUYVLDKoJj2QFuyMugIsxAEiInBi63lA/5ApkBQcgLuAn5Hc1pQUA2oX8hWupwMD3EGcgLkAITpQAkDApMagKDJwK4RjEBXzvp4lBXmhOYwDYUXCN4YbS7/9BVrA7r9kNcJHFixfv2rVr+PDhBjzWSy+9VF1dPWDAgJjuFQgEKC0gVhwzUKv/Y0qQhMsKSeoV4+sAERnVBYMcPXq0pKRE/n2aZGvZsuXAgQO3bt0a6x2V72q+DABI0KL6gXBZIXm9YtwdICLgMk06C3dBjz/96U+HDx9+//33DWtJv379Pvzwwx07dsR6R8V3RQ4PhJYyVnFjDNUFqN1QKhbVF6X1b6hfujBcL5LUXjHuDjAYl2mSUF0wwtatW+fNm/fQQw8Z+aDDhw/fuXPnK6+8kshGqDMDiMOi+kIIUb90ofjJN5AfJbtX1KUDhBJfH3UWMofedNNNmzZtKi0tDXkXIcQXX3zxwQcf/PKXv7zmmmvkhe+9996hQ4datGiRm5urWv+DDz744osvOnTokJmZqVw+Z86cyy67rG3bttLN9u3bnzx58uOPP9befmVpQf4XBwlUlNWFwGjz2gELOJZVqFpSv3SR+H4u1PdLgrsQVa8YUx+YvA4wJKoLEqoLSXfy5MkFCxZcd911Eda59NJLhw0b1qlTp507d0pL9u7d26lTp1GjRv3yl78MXv/IkSO9evV6+umnlQs3bNjQq1evtWvXyku6deu2a9eu+Gp9nFoJIIJjWYXSf8qF9UsXyVkhwn2De8WY+kADOkAEIy4k3fLly/1+f+S4kJaWNmvWLL/fX1JS4vf7/X5/cXFxVVXVzJkz09LSgtcvKipKT0+fNWuWcuFLL73k8Xj69u0rL2nVqpUQYvHixbG2WXqnBwIBLvgIQCU4JQghMo8ulIKCUGQFOTOo+o/gXjGmPjDZHSBCIi4k3bp164QQjRo1irxa27ZtR4wYsWvXrr///e9//etfd+7cOX78+JYtW4Zc2ePxlJSUHDx4cMOGDdKS6urq2bNnd+jQISvrx8u2t27dWgjxySefaGxqyEhAYgAgCQ4KmUcXSv/F1D+E7BW194FJ6gARRQC6ysvLUy0pKioSQpw/f15eUlNTc+6n5OXNmjXz+XxCiOuuuy7yA23btk0IMWjQIOnm7NmzhRAvvviiarXatWtnZmZqbLwQ3/8X6k8cMPiRGPPjf3C80vo3BP+nXCHCZ0rIXiW4V5Ro7wOT0QGGE9yruxPVhaSrqqoSQni9P14R67XXXrvgp6TlHo9nypQp0vr/+te/Im+2WbNmTZs2nTNnjt/vF0LMmDEjNTX1lltuUa3m8/kqKyu1tDPylRwDihoDZQbAJcKNO2QeXSjfjHyZ55DjEcG9okR7H6h7B4ioiAsmuOyyy4p+Sv7TxIkTpX+MGjUq6nZuv/32ioqKxYsXl5WVLVu2rKSkRErlKh6PPq9ygMmPgGtoCQoiCT8Job0PNLgDBBeBTrqLLrpICHH69Gl5wk7btm3lU32UXnrppXnz5g0ePPj8+fPTpk175ZVX+vTpE2HLffr0efDBB+fMmXP06FG/33/77bcHr/Pdd99puWiaxh+JCCiuEp2Swlm4gAOFTAnBq2kPCoGAel5UcK8oiakP1LEDhBbEhaSTDtYNGzZEPjni4MGDQ4cOzcnJGTdunBBi2bJld999d4cOHXJycsLdJT09vbCw8K233qqsrGzQoEFwBCkvL6+qqrr88sv12I/vkRgARwpOCSJMUBDxFhVSUr7/QhKyV4y1DzSlA3QzqjRJJx3Ee/bsibxacXHx6dOnX3jhhbS0tLS0tBdeeOH06dO9evWS/vrOO++kpKT88Y9/VN3rzjvv/O677xYvXhwyWUvTjzt06JD4XigxKgE4icZxB1niAxAhe8U4+kBTOkDXIi4k3TXXXFOvXr0VK1ZEWOeRRx7ZvHnzoEGDOnbsKC3p3Llz3759N23a9Pe//z3CHbt06VKvXj0hxG233Rb812XLlnk8HuXciJDi+LlqEgPgABFOjAx3l/iygmrCY3CvGF8fqEsHCI0oJuss5OVCx4wZ8+ijj5aWlkpHdnyWLl06ZcqURYsWqZZfdtlleXl5q1evVi33+/3169fv2LGj6mImweKICz/ckQtFuxQXgba1mMYdlBJ5y6v6mTh6xZB9YOIdYFRcBFpCdcEI9957b+3atZ9//vlENjJnzhzpImVKCxYsOHr0aL9+/UKuf/z4ce2/4BLHxz01BsBeYh13UNL360EcvWJwH6hjB4iomOpohIsvvnjEiBGTJk168MEHa9euHccWjh07dtFFFw0fPlxeMnTo0HPnzr3++uu5ubnBZxsLIcaNG9e/f/+os4IT/JRn5iNgC3FXFCSJZwX5/AhpwmOsvaKqD9SrA4R29O86C1e28vv9zZs3v/HGG8eMGaPLA7Vs2XLLli316tVbvHhxixYtVH999dVXhw8fvmPHjvT09MjbiXsk4qcbYVTCXRiMsBGNJ0ZGoNcbXNXbJNIr6tUBasFghITqgkE8Hs+yZct0POY2bNiwffv2Fi1ahLwISZMmTdauXavLW0ULagyA1SRYTpDp+GVAdQGGRHpFS3WALkHPrjN75VBdSguKrVFjcAuqC1amV1AQSXhT69vnGMNevXryUF2AbqgxAOZKfNxBRvqHCnEBelIlBkFHAySfjuUESfKyQvAFoWEXxAXoXBWUOhfKDDDR0qVLpV81DObxeHw+39VXX+2MgW3dg4Iwqq4gXxAadkFccK+kZnwGJmCiPn36lJeXR16nSZMmjz/+eNeuXY1pku6SERQEYxAIj7iAZGFgAuaqV69ekyZNVAuPHz++d+/e6urqXbt23XDDDTNmzLj11ltNaV7cdJygoEJWQATEBbdLap/AwARMdM0118yZMyd4ud/vf+GFF4YOHXr27Nm77rqrsLCwTp06xjcvVkkqJ0hUV2VN6vuU6Qs2xUWgXcrItyvXioaleDyeAQMGjB8/Xghx+vTppUuXmt2iKBK5crMWqqKCYZmezsBeqC7ACExlMNHatWsrKiqEEAUFBZF/zuf48eObNm0SQtSvX79ly5YGtc8kt9122z333COEWL169c0332x2c0JL3riDjAEIaERcgEGYymCWI0eO9O7dWwhx/fXXL1myJMKa/fr1W7p0qcfj2bhxo1GtM823334r/eOCCy4wtyXBkjruIDNyAAIOwGCEG5l1YTVVnZOBCWPceuutRUVFQoilS5e++uqr4VZ75ZVXpLL8yJEjW7dubVz7TDJ9+nTpH506dTK3JUrJHneQmTUA8cMjGvlo0AfVBRiNgQnjTZ06df369eXl5UOHDv39738fPCRRVlZ27733CiGaNWum16+gWVZVVdXTTz89evRoIUROTk5hYYiv8sYzYNxBZp0BCK6+YCPEBZiAgQmDZWRkPPvss8XFxRUVFUOGDHn99ddVKwwaNKiiosLn882dOzfkb/bY0bvvvvvHP/5RucTv9+/Zs+fw4cN+v18IkZGRsWDBAtP316ygIHjfIRbEBfcyt6PgHEuD9ezZc+7cufPnz583b978+fO7d+8u/+m1116bP3++EGLChAl5eXnmtVFnx44dO3bsWMg/ZWRk9O7de/jw4RkZGQa3SmbMBAUl6xQVYEf00Tqz/m+XWe0X4ejCDFNWVnbFFVeUlZVlZGTs27fv4osvFkKUl5dffvnlZWVlnTp1eueddzRuyuK/SHnJJZeUl5e3atVq8ODB0pLq6uoVK1a8/vrrfr+/qKjohRdekHbfFMYHBWHJN5rUImu0JRLr9+rGoLoAkzEwYZiMjIzJkycXFxeXlZX95S9/+c9//iOEuPfee8vKyurWrfvyyy+b3UCd/epXv+rTp498s1+/fkOGDPm///u/BQsWbNu2bdOmTZmZmQY3ychxB5nFByCYvmAXDhmkhK2p+i/OmEienj179ujRQwgxffr0rVu3rl27dubMmUKIKVOmZGVlmd26pGvbtu3s2bOFEAcPHuzSpcvp06eNeVzpfAdVVkjG+Q7BzD0DAk5CXHApq3UawedYEhqS5LnnnpMG7AcOHHjXXXcJIYqLiy17nSLdde3adciQIUKIXbt2Sf9IKsNOjAymehMRFJAg4gIshDKDAdLT05977jkhxPbt2/fu3ZuZmfnMM8+Y3ShDjRs3LicnRwjx8ssvr169OkmPEq6cYEBQEJYfgJBYslEIi7jgLtb//KXMYIDu3btLQxJCiJdeeik9Pd3c9hisdu3aU6dOlf49YMCAs2fP6rhxE8cdJMFFBWtmBSXe4rZAXIAVUWZItj/84Q/SP6655hpTG2KOLl269OrVSwjx3//+V7peU+JMHHeQ2aKoAJsiLsCiKDMgqZ5++mmprDJhwoSdO3cmsimLBAXbFRUE4xG2QlxwIxu9RQkNSJL09PRJkyYJIfx+v/QTXHEwd4KCJPhNYYugANvhuguwAeW1GQSXgEQ0X3/9tZbVbr311ltvvTWO7ZtynaWQHBMUuPqC9REXXMTWX8uDLxot7Nw5wqYICnAt4gLshDIDzGLKBRlDCh6P410AAxAXYDOUGWAk65QTJBQVYBbiAmyJ0IBkIygASpwZ4TpO6mS4PEPcBgwYIJ114vP5zG6L5VjhxEglZ5/74KBdcTiqC27h1E9SygzQkXUmKMgcHBRgL8QFOEHwFEhBxwrNrDbuIHFbUOBcSosjLsAhVGUGQWiABrYICoLDGBZAXICjEBqgkQXHHQRBARZGXHAXl/Q8hAaEY81ygiAowPKIC3AsQgOUCAqWFQg4di62kxAXXMHNb0VCA6w57iAICrAV4gJcgdDgTgQFe+HkCCsjLsBFCA0uYaNxB8HhB5sgLsB1CA0ORlAAkoS4AJciNDgM4w5AUhEX4GrhQoOgT7cJy5YTBEEBzkJcAEKEBkFusDyCgpNwLqX1EReA78kdesjcQHdvHTYadxAcOXAK4oKL0GtpRLHBmixbTgj3y+kcKnAS4gIQWuRig+DDwEAEBcB0xAUgCgYpTGTNoEBKgAsRF5yPCUR6YZDCSBacoEBKMAAXdrQs4gIQG4oNSWXBcgIpARDEBSBuIXMDxYa4WS0okBIAJeICkKjIgxSCD5hoLDXuQEoAQiIuAPoIN0ghiA5hWKqcQEoAIiMuADqLkBsE0UEIYZmgEC4iSFz76gAhEReAZFF+3kSODu75ZDI9KESOCMJNrwUQE+ICYITI0cENJQezJihEzQfCuc85oCPiAmA0V41WmFJOICIAuiMuAKbRPloR8i4WZ3BQICIASUVcACwhanQI9ycLfgQaMO6gJRwISz45gE0RFwDL0Rgdwq1g1mdkksoJGpOBjIgAJANxITaHDx/eu3fv//7v/+bn55vdFrhC8IefBQOEXkEh1mQgIyIAyUZciMHChQvHjRv3u9/97sMPP7zxxhvvvfdes1sEN9IlQMS0/chUWSFkSog7BwQjGThVIMDv4VkacUGrmpqaMWPGzJ07t2HDhuXl5Z06dSosLGzQoIHZ7QJCf4LG/Qmt6Y5jQjxi/dJF0v3je9xgJAPAOogLWr377rt169Zt2LChECI9Pb19+/YbN24Mjguffvqpjl+k9GXVdsH2vg8KerPsWwlJZbWXPS8vz+wmWAJxQauKiopGjRrJN3/+85/v27cveLW8vLyQy00kv/f4qoY4hP7MHpNSWv8G6Z/KrEA9AImQjjWrHUTMVJN4zG6AbdTU1Cj7zVq1atEzwg0CYcgpobT+DfJCc5sKIHmIC1r5fD6/3y/frKmpqVWrlontAUwnz2oMeWYEACchLmh16aWX7tq1S75ZUVHRvHlzE9sDWAGJAXqx2pQFqBAXtGrZsqUQYt26dUKIzz77bOPGjQUFBWY3CjAfiQFwA6Y6auXxeJ544okHHnggNzd3165d48aNy8jIMLtRgCVkHl0oZYVjWYVG/ho1AMOkMDtJX/n5+ZwZATdISVH3HnJ1gcSAOFi2p7Jgr24KBiMA6INRCcDBiAsAdENiAJyKuABATyQGwJGICwB0RmIAnIe4AEB/JAbAYYgLAJKCxAA4CXEBQLKQGADHIC4ASCISA+AMxAXns9o1T+A2JAbAAYgLAJKOxADYHXEBgBFIDNCCaqhlERdchN+HhblIDIB9ERcAGIfEgJD4MmN9xAUAhiIxAHZEXABgNBIDYDvEBQAmIDEA9kJcAGAOEgNgI8QFAKYhMUCJsyitjLjgCrwJYVkkBvz/9u4/tqqrAOD4pV02BTTMrjZIIlmQMStTgRiShqnZxpYlVWd0zh8gcdkvEcVkMRqziEm36Ji4qYkmqFsyJTgXJcFkJqiMwRxzOiSMsbWI8iNjK644FRYCbZ9/PHyU/rrte/e9e+69n0/2R0s7evJ497zvO+e8VzJBLgApUwwQPrkApE8xFJk3XcgEuVAsLkuCpRggZHIBCIVigGDJBSAgigHCJBeAsCgGCJBcAIKjGArI670DJxeKwqVItigGCIpcKBwvjiArFEMRmJGyQi4A4VIMEAi5AARNMUAI5EKBOL5ARikGSJ1cADJAMeSbJzPhkwtF5GwRWaQY8sdclCFyAcgMxQBpkQtAligGSIVcKBYbhOSAYsgZ81ImyIWCsmVIpimGHDALZYtcADJJMUAjyQUgqxQDNIxcADJMMWSdgwtZIRcKx8VJziiGLHJwIXPkQnG5XMkNxQD1JheAPFAMUFdyAcgJxQD1IxeKyPEF8koxZIu5KEPkQqE5vkD+KIbwmXmySC4AeaMYIHFyoaCsAZJvigGSJReKzqogeaUYAudJS7bIBSC3FEOAPEXJKLkA5JligETIheKqrASKffJNMYSjMtvYicgcuQDkn2KAGskFoBAUA9RCLhSa/QgKRTGky05EpskFoEAUA1RHLgDFohigCnKh6OxHUECKofHsRGSdXACKSDHApMgFoKAUA0ycXMDaIMWlGBrDTkQOyAXOcXyBAlIMMBFyASg6xQCx5AJR5PURFJ5iqB87EfkgFwCiSDHAuOQCZwl/UAz1Y4bJOrnAcPYjKDLFkCzzSW7IBYDzKAYYSS5wjgOPUKYYEuGQY57IBYBRKAYYSi5wHgsMUKEYamFpIWfkAsCYFAOUyQWG81QAhlIMtTCf5IZcYEz2I6BMMUyW2SN/5AJAPMVAwckFRuHAI4ykGCbIIcdckgsAE6UYKCy5wOgsMMCoFMP4LC3klVwAmBzFQAHJBcZkgQHGohhGZWkhx+QCQDUUA4UiF5gQCwwwkmIYytJCvskFxuOyh/EpBgrigrQHQOhKpbNPGqZMUQ9kw2OPPXb69OlRv9TU1HThhRe+733va2lpSerHzXxpc7kVXp714Uo9FI2lhdyTC0DefPazn+3r6xv/e+bPn/+tb32rs7MzkZ+oGMi9KSUpmKh58+Z1d3enPYrkeerAMFOmhDt7XHLJJX19fW1tbfPnzx/2pd7e3hdffLG/v7/86c9+9rNly5Yl9XMr+xFFK4Z8zw95ndUnK9wLPqPyesfK93RAFcLPhZtuuukXv/jFyK8ODg4++OCDX/ziF0+dOjV9+vSXXnrpzW9+c1I/upjFkO/5Ia+z+mQ56siEeA8GcqOpqemWW25Zu3ZtFEUnTpx47LHHEvzLC3jyMd+tQIVcmJz9+/f/7ne/27VrV9oDAWqyYsWK8gdbt25N9m8uYDFQBI46TkJXV9fjjz++aNGi7u7u6dOnP/TQQxdddFHag2ocL5EgT06ePFn+oB5XcXFOPlpaKA6rCxO1b9++Rx555Fe/+tV99923efPm//73v7/5zW/SHlSj2ZIgN37605+WP7j66qvr8fcXYY3BPFAocmGiZsyYsX79+osvvrj86aWXXnr06NF0hwRU4fTp0+vWrVuzZk0URbNnz/7wh+v1cF6EYiiztFAE4Z5tDtnBgwc7Ozt/+ctftre3D/vSvHnzRn5/zk7VWn4kysIrI2bOnLlgwYKhfz44OPjCCy8cOXJkcHAwiqLW1tYtW7a8973vretg8vpaibzOA0WYw6sT7gUfrN7e3k9+8pM33njjypUrR361CC+5yes0waSEnwvjfENra+vy5cu/9rWvtba2NmA8uSyG4swDRZjVJ8JRx/F0dXVt2rQpiqJp06bt2LEjiqI9e/bcfvvtt956680335z26FLjzCOZsHjx4krT9/f3b9my5dFHHx0cHLzhhhsefPDBysZiA+Tv5GNxWoGKcJ8fhODAgQO9vb1RFDU3Ny9evPipp55avXr13Xfffd111431vxSkQ00WhL+6MPJtmp588snrr7/+xIkTs2fP3rlz58yZMxs5qjytMRRqBijIrB7LUcfxzJkzp6Ojo6OjY/HixUeOHFm1atXatWuvuuqqM2fOnDlzZmBgIO0BpsZLJMiiJUuWbNy4MYqiQ4cOXXvttSdOnGjkT8/NycdCtQIVcmGiNmzYcPLkyTvuuGP+/91zzz1pDwqYnM7OzlWrVkVRtHfv3vIHjZSDYtAKhRXucmJGFWrZysRRZFncjCh7/fXX29vbDx06FEXRH/7wh6uuuqrBw8v0rkQBr/pCzerjsLpA9WxJkEVTp05dv359+eNbbrnl1KlTDR5AdtcYCtgKVMgFkqEYyJBrr732U5/6VBRF//jHP8rv19Rg2S0GCksuUBNPMsioH/zgBy0tLVEUfec739mzZ0/jB5C5YrC0UHBygVrZkiCLWlpaHnjggSiKBgcHly9fnsoYMlQMWoFwDytlVDEPxQwNBXeoggj5qGO2ZOLkY5FzoZiz+khWF0hAAWcQSEr4awxFbgUq5ALJsCUBVQu5GLQCZXKB5CkGmDMq3mAAAAy5SURBVKwwi8G1TIVcIDGefEAtwiyGMlc3coEk2ZKAWgRVDLYhGEoukDDFALUIpBi0AsPIBepIMUAVUi8GVy4jyQWS5+kI1Cj1YihzLVMhF6gLWxJQo7SKwTYEo5IL1J1igOo0vhi0AmORC9SL6QZq18hiUPaMQy5QR7YkoHaNX2PQ+owkF6gvxQC1a0Ax2IZgfHKBxlEMULW6FoNrk1hygbob+mTFrARVq1Mx+AX0TIRcoBEUAyQi8WLQCkyQXKBBFAMkok5rDFqB8ckFGsd8BIlIqhgcb2Ti5AIN5YUSkIjai0ErMClygUZTDJCIWopBKzBZcoE0KQaoRXXF4LqjCnKBFDj2CEmZbDF4KQTVkQukQzFAUiZeDFqBqskFUqMYICkTKQatQC3kAmkyZ0FSxi8GrUCN5AIp80IJSMpYxaAVqJ1cIH2KAZIy/hqDVqBqcoEgKAZIyrBi8BYLJEIuEIqhxSAaoBYj1xi0AjWSCwTEayUgKZViiLQCSbgg7QHAeUqlc6EwZYppDqo0ZUoURZsjrUBCrC4QHGsMUIuh23lagaTIBUKkGKA6XjNJncgFAqUYYLK0AvUjFwiXYoCJ0wrUlVwgaIoBJkIrUG9ygdApBhifVqAB5AIZoBhgLFqBxpALZINigJG0Ag0jF8gMxQBDaQUaSS6QJcOKQTRQWEPfiEkr0ABygYwZNjkqBorGmzaSCrlAJikGiskGBGmRC2SVYqBotAIpkgtkmKMMFMSwu7dWoPHkAtnmKAO5N+xerRVIhVwgDxQDeTVsUUErkBa5QE7YmCBnbEAQFLlAftiYIDcsKhAauUDeKAayzqICAZIL5JBiIKNsQBAsuUA+OcpA5tiAIGRygdwaeZRBNBAsiwoETi6Qc8NmXsVAaGxAkAkXpD0AqLvy/FuZkcsfmJQJgVAgK6wuUBSWGQiKRQWyxeoCBWKZgRB4U2eyyOoChWOZgRRpBTLK6gJFZJmBxhMKZJpcoLhEA40hFMgBmxEUnb0J6mfku31oBTLK6gJYZqAuhAJ5IhfgrFLpvPldNFA1oUD+yAU4Z9gyQyQamKSRm1nuPOSDXIDhRANVEArkm1yA0YkGJkgoUARyAcYjGhiHUKA45ALEEw0MIxQoGrkAEyUaiIQCRSUXYHJEQ2EJBYpMLkA1REOhCAWQC1C9saIh8nCSC6O+I7h/WYpJLkCtRkZDpBsyTijAMHIBklF5LBm1GzzSZIJKgLHIBUiYxYbMGevXkPrHggq5AHVhsSF8KgEmTi5AfY3aDRYbUjRWJUT+OWBscgEaxCZF6iwnQNXkAjTU+JsUw76HRKgEqJ1cgHSMuthQJh1qZ8cBkiUXIE1DH7rGTwcPcrHGSYTIDQi1aUp7ADTCvHnz0h7CcAEOKUp7VKXSuf9GmjLl3H+UDb1NxtlxGOsmbRj39gkKcEhUWF2AEI2/6jDsTwr1vHkitVSoGwQaw+oChO6yy+aN//x42JPsnC0/TGoJoXxbAYmTC9XYvXv3P//5z7RHQeGMv1sxVEYDYuSwxz+xGMJGAxSEXJi0/fv3L1u2bPfu3WkPhEIb+mA5kcfLST0SN0B145E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