{"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":44386,"title":"Circumscribed Pentagon?","description":"Building off of \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44368 Problem 44368\u003e, your function will be provided with the five vertices of a regular pentagon (p) as well as the center point (cp) and radius (r) of a circle. The function should return one of the following values:\r\n\r\n  0: the pentagon is completely enclosed within the circle but is not inscribed\r\n  1: the pentagon is inscribed in the circle (within ±0.02)\r\n  2: the vertices of the pentagon extend beyond the circle, but its edges still cross back into the circle\r\n  3: the pentagon circumscribes the circle (within ±0.02)\r\n  4: the pentagon completely encloses, and does not touch, the circle\r\n\r\nPoints will be rounded to the nearest hundredth. See the test cases for examples.","description_html":"\u003cp\u003eBuilding off of \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44368\"\u003eProblem 44368\u003c/a\u003e, your function will be provided with the five vertices of a regular pentagon (p) as well as the center point (cp) and radius (r) of a circle. The function should return one of the following values:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e0: the pentagon is completely enclosed within the circle but is not inscribed\r\n1: the pentagon is inscribed in the circle (within ±0.02)\r\n2: the vertices of the pentagon extend beyond the circle, but its edges still cross back into the circle\r\n3: the pentagon circumscribes the circle (within ±0.02)\r\n4: the pentagon completely encloses, and does not touch, the circle\r\n\u003c/pre\u003e\u003cp\u003ePoints will be rounded to the nearest hundredth. See the test cases for examples.\u003c/p\u003e","function_template":"function y = circumscribed_pentagon(p,cp,r)\r\n  y = 0;\r\nend","test_suite":"%%\r\np = [0,5; 4.76,1.55; 2.94,-4.05; -2.94,-4.05; -4.76,1.55];\r\ncp = [0,0];\r\nr = 5;\r\ny_correct = 1;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [0,5.61; 5.40,1.69; 3.34,-4.66; -3.34,-4.66; -5.40,1.69];\r\ncp = [0,0];\r\nr = 5;\r\ny_correct = 2;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [0,6.18; 5.88,1.91; 3.63,-5.00; -3.63,-5.00; -5.88,1.91];\r\ncp = [0,0];\r\nr = 5;\r\ny_correct = 3;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [0,4.55; 4.28,1.44; 2.65,-3.59; -2.65,-3.59; -4.28,1.44];\r\ncp = [0,0];\r\nr = 5;\r\ny_correct = 0;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\ncp = [20,8];\r\np = [0,5; 4.76,1.55; 2.94,-4.05; -2.94,-4.05; -4.76,1.55] + repmat(cp,[5,1]);\r\nr = 5;\r\ny_correct = 1;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [20,13.61; 25.40,9.69; 23.34,3.34; 16.66,3.34; 14.60,9.69];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 2;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [20,14.18; 25.88,9.91; 23.63,3.00; 16.37,3.00; 14.12,9.91];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 3;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\ncp = [20,8];\r\np = [0,6.58; 6.42,1.92; 3.97,-5.63; -3.97,-5.63; -6.42,1.92] + repmat(cp,[5,1]);\r\nr = 5;\r\ny_correct = 4;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\ncp = [20,8];\r\np = [0,4.55; 4.28,1.44; 2.65,-3.59; -2.65,-3.59; -4.28,1.44] + repmat(cp,[5,1]);\r\nr = 5;\r\ny_correct = 0;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [23.66,11.42; 24.37,5.58; 19.05,3.10; 15.04,7.40; 17.89,12.54];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 1;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [25.01,12.47; 25.98,4.58; 18.78,1.23; 13.37,7.03; 17.22,13.97];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 4;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [23.27,11.12; 23.92,5.87; 19.12,3.63; 15.52,7.50; 18.08,12.13];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 0;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [30.94,36.26; 35.61,27.09; 28.34,19.82; 19.17,24.49; 20.78,34.65];\r\ncp = [26.97,28.45];\r\nr = 8.75;\r\ny_correct = 1;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [32.54,38.78; 38.84,26.41; 29.02,16.59; 16.65,22.89; 18.83,36.61];\r\ncp = [26.97,28.45];\r\nr = 8.75;\r\ny_correct = 4;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [30.49,35.54; 34.69,27.29; 28.14,20.74; 19.89,24.95; 21.34,34.09];\r\ncp = [26.97,28.45];\r\nr = 8.75;\r\ny_correct = 0;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [26.97,34.06; 32.37,30.14; 30.31,23.79; 23.63,23.79; 21.57,30.14];\r\ncp = [26.97,28.45];\r\nr = 5;\r\ny_correct = 2;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [31.35,32.83; 32.49,25.64; 26.00,22.34; 20.85,27.48; 24.16,33.97];\r\ncp = [26.97,28.45];\r\nr = 5.01;\r\ny_correct = 3;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":64,"test_suite_updated_at":"2017-12-08T15:45:11.000Z","rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-13T20:03:45.000Z","updated_at":"2025-11-04T13:12:51.000Z","published_at":"2017-10-16T01:51:02.000Z","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:t\u003eBuilding off of\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/44368\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 44368\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, your function will be provided with the five vertices of a regular pentagon (p) as well as the center point (cp) and radius (r) of a circle. The function should return one of the following values:\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[0: the pentagon is completely enclosed within the circle but is not inscribed\\n1: the pentagon is inscribed in the circle (within ±0.02)\\n2: the vertices of the pentagon extend beyond the circle, but its edges still cross back into the circle\\n3: the pentagon circumscribes the circle (within ±0.02)\\n4: the pentagon completely encloses, and does not touch, the circle]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePoints will be rounded to the nearest hundredth. See the test cases for examples.\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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":44386,"title":"Circumscribed Pentagon?","description":"Building off of \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44368 Problem 44368\u003e, your function will be provided with the five vertices of a regular pentagon (p) as well as the center point (cp) and radius (r) of a circle. The function should return one of the following values:\r\n\r\n  0: the pentagon is completely enclosed within the circle but is not inscribed\r\n  1: the pentagon is inscribed in the circle (within ±0.02)\r\n  2: the vertices of the pentagon extend beyond the circle, but its edges still cross back into the circle\r\n  3: the pentagon circumscribes the circle (within ±0.02)\r\n  4: the pentagon completely encloses, and does not touch, the circle\r\n\r\nPoints will be rounded to the nearest hundredth. See the test cases for examples.","description_html":"\u003cp\u003eBuilding off of \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44368\"\u003eProblem 44368\u003c/a\u003e, your function will be provided with the five vertices of a regular pentagon (p) as well as the center point (cp) and radius (r) of a circle. The function should return one of the following values:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e0: the pentagon is completely enclosed within the circle but is not inscribed\r\n1: the pentagon is inscribed in the circle (within ±0.02)\r\n2: the vertices of the pentagon extend beyond the circle, but its edges still cross back into the circle\r\n3: the pentagon circumscribes the circle (within ±0.02)\r\n4: the pentagon completely encloses, and does not touch, the circle\r\n\u003c/pre\u003e\u003cp\u003ePoints will be rounded to the nearest hundredth. See the test cases for examples.\u003c/p\u003e","function_template":"function y = circumscribed_pentagon(p,cp,r)\r\n  y = 0;\r\nend","test_suite":"%%\r\np = [0,5; 4.76,1.55; 2.94,-4.05; -2.94,-4.05; -4.76,1.55];\r\ncp = [0,0];\r\nr = 5;\r\ny_correct = 1;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [0,5.61; 5.40,1.69; 3.34,-4.66; -3.34,-4.66; -5.40,1.69];\r\ncp = [0,0];\r\nr = 5;\r\ny_correct = 2;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [0,6.18; 5.88,1.91; 3.63,-5.00; -3.63,-5.00; -5.88,1.91];\r\ncp = [0,0];\r\nr = 5;\r\ny_correct = 3;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [0,4.55; 4.28,1.44; 2.65,-3.59; -2.65,-3.59; -4.28,1.44];\r\ncp = [0,0];\r\nr = 5;\r\ny_correct = 0;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\ncp = [20,8];\r\np = [0,5; 4.76,1.55; 2.94,-4.05; -2.94,-4.05; -4.76,1.55] + repmat(cp,[5,1]);\r\nr = 5;\r\ny_correct = 1;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [20,13.61; 25.40,9.69; 23.34,3.34; 16.66,3.34; 14.60,9.69];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 2;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [20,14.18; 25.88,9.91; 23.63,3.00; 16.37,3.00; 14.12,9.91];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 3;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\ncp = [20,8];\r\np = [0,6.58; 6.42,1.92; 3.97,-5.63; -3.97,-5.63; -6.42,1.92] + repmat(cp,[5,1]);\r\nr = 5;\r\ny_correct = 4;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\ncp = [20,8];\r\np = [0,4.55; 4.28,1.44; 2.65,-3.59; -2.65,-3.59; -4.28,1.44] + repmat(cp,[5,1]);\r\nr = 5;\r\ny_correct = 0;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [23.66,11.42; 24.37,5.58; 19.05,3.10; 15.04,7.40; 17.89,12.54];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 1;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [25.01,12.47; 25.98,4.58; 18.78,1.23; 13.37,7.03; 17.22,13.97];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 4;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [23.27,11.12; 23.92,5.87; 19.12,3.63; 15.52,7.50; 18.08,12.13];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 0;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [30.94,36.26; 35.61,27.09; 28.34,19.82; 19.17,24.49; 20.78,34.65];\r\ncp = [26.97,28.45];\r\nr = 8.75;\r\ny_correct = 1;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [32.54,38.78; 38.84,26.41; 29.02,16.59; 16.65,22.89; 18.83,36.61];\r\ncp = [26.97,28.45];\r\nr = 8.75;\r\ny_correct = 4;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [30.49,35.54; 34.69,27.29; 28.14,20.74; 19.89,24.95; 21.34,34.09];\r\ncp = [26.97,28.45];\r\nr = 8.75;\r\ny_correct = 0;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [26.97,34.06; 32.37,30.14; 30.31,23.79; 23.63,23.79; 21.57,30.14];\r\ncp = [26.97,28.45];\r\nr = 5;\r\ny_correct = 2;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))\r\n\r\n%%\r\np = [31.35,32.83; 32.49,25.64; 26.00,22.34; 20.85,27.48; 24.16,33.97];\r\ncp = [26.97,28.45];\r\nr = 5.01;\r\ny_correct = 3;\r\nassert(isequal(circumscribed_pentagon(p,cp,r),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":64,"test_suite_updated_at":"2017-12-08T15:45:11.000Z","rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-13T20:03:45.000Z","updated_at":"2025-11-04T13:12:51.000Z","published_at":"2017-10-16T01:51:02.000Z","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:t\u003eBuilding off of\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/44368\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 44368\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, your function will be provided with the five vertices of a regular pentagon (p) as well as the center point (cp) and radius (r) of a circle. 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