{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","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":"2026-05-26T00:00:00.000Z","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":58354,"title":"Find the circle inscribed in a triangle","description":"Write a function that takes the x- and y-coordinates of three points describing the vertices of a triangle and returns the center and radius of a circle inscribed in the triangle (i.e., tangent to each of the three sides).","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: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"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: 365.1px 8px; transform-origin: 365.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the x- and y-coordinates of three points describing the vertices of a triangle and returns the center and radius of a circle inscribed in the triangle (i.e., tangent to each of the three sides).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [x0,y0,r] = incircle(x,y)\r\n%  x = vector of x-coordinates of the triangle's vertices\r\n%  y = vector of y-coordinates of the triangle's vertices\r\n%  (x0,y0) = coordinates of the incircle's center\r\n%  r = radius of the incircle\r\n   [x0,y0,r] = Delaunay(something(x),something(y));\r\nend","test_suite":"%%\r\nx = [0 1 0];\r\ny = [0 0 1];\r\nx0_correct = 0.29289321881;\r\ny0_correct = 0.29289321881;\r\nr_correct = 0.29289321881;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nth = pi/2:2*pi/3:11*pi/6;\r\nx = cos(th);\r\ny = sin(th);\r\nx0_correct = 0;\r\ny0_correct = 0;\r\nr_correct = 0.5;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [1 4 5];\r\ny = [2 3 6];\r\nx0_correct = 3.47213595500;\r\ny0_correct = 3.52786404500;\r\nr_correct = 0.66770107084;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [1 4 5];\r\ny = [2 3 6];\r\nx0_correct = 3.47213595500;\r\ny0_correct = 3.52786404500;\r\nr_correct = 0.66770107084;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [-1 4 5];\r\ny = [2 -3 6];\r\nx0_correct = 2.36290232380;\r\ny0_correct = 1.66700704764;\r\nr_correct = 2.14246946292;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [12 3 45];\r\ny = [6 78 9];\r\nx0_correct = 23.24160585487;\r\ny0_correct = 19.96162835361;\r\nr_correct = 12.88652365580;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [-1 0 1];\r\ny = [0 19 0];\r\nx0_correct = 0;\r\ny0_correct = 0.94875250476;\r\nr_correct = 0.94875250476;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [10 15 20];\r\ny = [30 45.1 60];\r\nx0_correct = 15.01499995500; \r\ny0_correct = 45.09499981499; \r\nr_correct = 0.01581137249;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nL = 100*rand;\r\nx = [0 L 0];\r\ny = [0 0 L];\r\nd_correct = L/(2+sqrt(2)); \r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-d_correct)\u003c1e-10)\r\nassert(abs(y0-d_correct)\u003c1e-10)\r\nassert(abs(r-d_correct)\u003c1e-10)\r\n\r\n%%\r\nfiletext = fileread('incircle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-05-20T15:34:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-20T15:33:53.000Z","updated_at":"2026-04-24T14:41:02.000Z","published_at":"2023-05-20T15:34:18.000Z","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\u003eWrite a function that takes the x- and y-coordinates of three points describing the vertices of a triangle and returns the center and radius of a circle inscribed in the triangle (i.e., tangent to each of the three sides).\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\"}]}"}],"problem_search":{"problems":[{"id":58354,"title":"Find the circle inscribed in a triangle","description":"Write a function that takes the x- and y-coordinates of three points describing the vertices of a triangle and returns the center and radius of a circle inscribed in the triangle (i.e., tangent to each of the three sides).","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: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"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: 365.1px 8px; transform-origin: 365.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the x- and y-coordinates of three points describing the vertices of a triangle and returns the center and radius of a circle inscribed in the triangle (i.e., tangent to each of the three sides).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [x0,y0,r] = incircle(x,y)\r\n%  x = vector of x-coordinates of the triangle's vertices\r\n%  y = vector of y-coordinates of the triangle's vertices\r\n%  (x0,y0) = coordinates of the incircle's center\r\n%  r = radius of the incircle\r\n   [x0,y0,r] = Delaunay(something(x),something(y));\r\nend","test_suite":"%%\r\nx = [0 1 0];\r\ny = [0 0 1];\r\nx0_correct = 0.29289321881;\r\ny0_correct = 0.29289321881;\r\nr_correct = 0.29289321881;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nth = pi/2:2*pi/3:11*pi/6;\r\nx = cos(th);\r\ny = sin(th);\r\nx0_correct = 0;\r\ny0_correct = 0;\r\nr_correct = 0.5;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [1 4 5];\r\ny = [2 3 6];\r\nx0_correct = 3.47213595500;\r\ny0_correct = 3.52786404500;\r\nr_correct = 0.66770107084;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [1 4 5];\r\ny = [2 3 6];\r\nx0_correct = 3.47213595500;\r\ny0_correct = 3.52786404500;\r\nr_correct = 0.66770107084;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [-1 4 5];\r\ny = [2 -3 6];\r\nx0_correct = 2.36290232380;\r\ny0_correct = 1.66700704764;\r\nr_correct = 2.14246946292;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [12 3 45];\r\ny = [6 78 9];\r\nx0_correct = 23.24160585487;\r\ny0_correct = 19.96162835361;\r\nr_correct = 12.88652365580;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [-1 0 1];\r\ny = [0 19 0];\r\nx0_correct = 0;\r\ny0_correct = 0.94875250476;\r\nr_correct = 0.94875250476;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [10 15 20];\r\ny = [30 45.1 60];\r\nx0_correct = 15.01499995500; \r\ny0_correct = 45.09499981499; \r\nr_correct = 0.01581137249;\r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-x0_correct)\u003c1e-10)\r\nassert(abs(y0-y0_correct)\u003c1e-10)\r\nassert(abs(r-r_correct)\u003c1e-10)\r\n\r\n%%\r\nL = 100*rand;\r\nx = [0 L 0];\r\ny = [0 0 L];\r\nd_correct = L/(2+sqrt(2)); \r\n[x0,y0,r] = incircle(x,y);\r\nassert(abs(x0-d_correct)\u003c1e-10)\r\nassert(abs(y0-d_correct)\u003c1e-10)\r\nassert(abs(r-d_correct)\u003c1e-10)\r\n\r\n%%\r\nfiletext = fileread('incircle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-05-20T15:34:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-20T15:33:53.000Z","updated_at":"2026-04-24T14:41:02.000Z","published_at":"2023-05-20T15:34:18.000Z","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\u003eWrite a function that takes the x- and y-coordinates of three points describing the vertices of a triangle and returns the center and radius of a circle inscribed in the triangle (i.e., tangent to each of the three sides).\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\"}]}"}],"errors":[],"facets":[[],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"incircle\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}