{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":1336,"title":"Geometry: Find Circle given 3 Non-Colinear Points","description":"*This Challenge is to determine the center and radius of a circle given three non-colinear points.*\r\n\r\n*Input:* Points\r\n\r\n*Output:* [xc, yc, r] where [xc,yc] are the center and r is the radius\r\n\r\n*Example:*\r\n\r\nInput: Points = [1 0 ; 0 -1 ; 0 1]\r\n\r\nOutput: [ 0 0 1]\r\n\r\n*Theory/Hint:* The Kasa method provides a best fit circle to a set of points.\r\n\r\n*Future:* 1) Circumscribe 4 points  2) Circumscribe N points  3) The Great Lego Cup Challenge","description_html":"\u003cp\u003e\u003cb\u003eThis Challenge is to determine the center and radius of a circle given three non-colinear points.\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e Points\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [xc, yc, r] where [xc,yc] are the center and r is the radius\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eInput: Points = [1 0 ; 0 -1 ; 0 1]\u003c/p\u003e\u003cp\u003eOutput: [ 0 0 1]\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory/Hint:\u003c/b\u003e The Kasa method provides a best fit circle to a set of points.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFuture:\u003c/b\u003e 1) Circumscribe 4 points  2) Circumscribe N points  3) The Great Lego Cup Challenge\u003c/p\u003e","function_template":"function [xc,yc,r]=find_circle(pts)\r\n xc=0;\r\n yc=0;\r\n r=1;\r\n\r\n","test_suite":"%%\r\nfor tests=1:5\r\n xc_truth=randn;\r\n yc_truth=randn;\r\n r_truth=rand;\r\n rand_ang=randi(360,3,1)+rand(3,1); % Avoid duplicate location via rand(3,1)\r\n pts=[xc_truth+r_truth*cosd(rand_ang) yc_truth+r_truth*sind(rand_ang)]; \r\n\r\n [xc,yc,r]=find_circle(pts);\r\n\r\n %dif=[xc yc r]-[xc_truth yc_truth r_truth]\r\n\r\n assert(max(abs([xc,yc,r]-[xc_truth,yc_truth,r_truth]))\u003c1e-6,...\r\nsprintf('Expect xc %.2f yc %.2f r %.2f  Ans:%.2f %.2f %.2f',...\r\n  xc_truth,yc_truth,r_truth,xc,yc,r))\r\nend","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":64,"test_suite_updated_at":"2017-02-24T17:19:01.000Z","rescore_all_solutions":false,"group_id":20,"created_at":"2013-03-10T17:26:14.000Z","updated_at":"2026-02-16T11:13:15.000Z","published_at":"2013-03-10T18:03:52.000Z","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\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"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\\n\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis Challenge is to determine the center and radius of a circle given three non-colinear points.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Points\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [xc, yc, r] where [xc,yc] are the center and r is the radius\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: Points = [1 0 ; 0 -1 ; 0 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: [ 0 0 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory/Hint:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e The Kasa method provides a best fit circle to a set of points.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFuture:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 1) Circumscribe 4 points 2) Circumscribe N points 3) The Great Lego Cup Challenge\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\\\" 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Challenge","description_html":"\u003cp\u003e\u003cb\u003eThis Challenge is to determine the center and radius of a circle given three non-colinear points.\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e Points\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [xc, yc, r] where [xc,yc] are the center and r is the radius\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eInput: Points = [1 0 ; 0 -1 ; 0 1]\u003c/p\u003e\u003cp\u003eOutput: [ 0 0 1]\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory/Hint:\u003c/b\u003e The Kasa method provides a best fit circle to a set of points.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFuture:\u003c/b\u003e 1) Circumscribe 4 points  2) Circumscribe N points  3) The Great Lego Cup Challenge\u003c/p\u003e","function_template":"function [xc,yc,r]=find_circle(pts)\r\n xc=0;\r\n yc=0;\r\n r=1;\r\n\r\n","test_suite":"%%\r\nfor tests=1:5\r\n xc_truth=randn;\r\n yc_truth=randn;\r\n r_truth=rand;\r\n rand_ang=randi(360,3,1)+rand(3,1); % Avoid duplicate location via rand(3,1)\r\n pts=[xc_truth+r_truth*cosd(rand_ang) yc_truth+r_truth*sind(rand_ang)]; \r\n\r\n [xc,yc,r]=find_circle(pts);\r\n\r\n %dif=[xc yc r]-[xc_truth yc_truth r_truth]\r\n\r\n assert(max(abs([xc,yc,r]-[xc_truth,yc_truth,r_truth]))\u003c1e-6,...\r\nsprintf('Expect xc %.2f yc %.2f r %.2f  Ans:%.2f %.2f %.2f',...\r\n  xc_truth,yc_truth,r_truth,xc,yc,r))\r\nend","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":64,"test_suite_updated_at":"2017-02-24T17:19:01.000Z","rescore_all_solutions":false,"group_id":20,"created_at":"2013-03-10T17:26:14.000Z","updated_at":"2026-02-16T11:13:15.000Z","published_at":"2013-03-10T18:03:52.000Z","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\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"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\\n\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis Challenge is to determine the center and radius of a circle given three non-colinear points.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Points\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [xc, yc, r] where [xc,yc] are the center and r is the radius\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: Points = [1 0 ; 0 -1 ; 0 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: [ 0 0 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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