{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-08-24T00:15:41.000Z","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":"2026-08-24T00:00:00.000Z","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":61449,"title":"Geometry time3!(Medium)","description":"This time we have two circles! The shape is given below:\r\n\r\nYou are requested to calculate the area of the two circles(A1 ,A2) given the distance O1O2 = a, the distance D and that both the angle O1AB and O2BA are 90 degrees.\r\nExplanation(if needed):O1O2 is the line that connects the centers of both circles.\r\nTips:1) You can draw a line somewhere on this shape if you want.\r\n2) The circles are tangent.\r\nGOOD LUCK!!!!!!!!!!!!!!!!!!!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 407.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 203.9px; transform-origin: 469px 203.9px; vertical-align: baseline; \"\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis time we have two circles! The shape is given below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 206.8px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 103.4px; text-align: left; transform-origin: 445px 103.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"309\" height=\"201\" style=\"vertical-align: baseline;width: 309px;height: 201px\" 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\" data-image-state=\"image-loaded\"\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are requested to calculate the area of the two circles(A1 ,A2) given the distance O1O2 = a, the distance D and that both the angle O1AB and O2BA are 90 degrees.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eExplanation(if needed):O1O2 is the line that connects the centers of both circles.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eTips:1) You can draw a line somewhere on this shape if you want.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003e2) The circles are tangent.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [A1,A2] = find_the_circles_area(a,D)\r\n  \r\nend","test_suite":"%%\r\na = 7;\r\nD = 6;\r\nA1_exp = (pi*(7 + sqrt(13))^2)/4;\r\nA2_exp = (pi*(7 - sqrt(13))^2)/4;\r\n[A1_act, A2_act] = find_the_circles_area(a, D);\r\nassert(abs(A1_act - A1_exp) \u003c 1e-4, 'A1 is wrong.');\r\nassert(abs(A2_act - A2_exp) \u003c 1e-4, 'A2 is wrong.');\r\n%%\r\nD_val = randi([5, 50]);\r\na_val = D_val + randi([1, 20]);\r\nd = sort(roots([1, -2*a_val, D_val^2]), 'descend');\r\nA1_ref = (pi/4) * d(1)^2;\r\nA2_ref = (pi/4) * d(2)^2;\r\n[A1_user, A2_user] = find_the_circles_area(a_val, D_val);\r\nassert(abs(A1_user - A1_ref) \u003c 1e-4, 'A1 is wrong.');\r\nassert(abs(A2_user - A2_ref) \u003c 1e-4, 'A2 is wrong.');","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5158730,"edited_by":5158730,"edited_at":"2026-08-23T22:22:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-08-23T22:20:50.000Z","updated_at":"2026-08-27T13:35:31.000Z","published_at":"2026-08-23T22:20:50.000Z","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\u003eThis time we have two circles! The shape is given below:\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=\\\"201\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"309\\\"/\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\u003eYou are requested to calculate the area of the two circles(A1 ,A2) given the distance O1O2 = a, the distance D and that both the angle O1AB and O2BA are 90 degrees.\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:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation(if needed):O1O2 is the line that connects the centers of both circles.\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:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTips:1) You can draw a line somewhere on this shape if you want.\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:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2) The circles are 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44817,"title":"Wrecked Angles?","description":"It's time for some simple geometry fun to start off the new year.\r\n\r\nYou will be given the perimeter P and the area A of a rectangle.  With these two values, calculate the area of the circle that circumscribes this rectangle.  This means we're looking for the area of the circle that touches this rectangle only at the four vertices of the rectangle.\r\n\r\nGood luck, and Happy 2019!","description_html":"\u003cp\u003eIt's time for some simple geometry fun to start off the new year.\u003c/p\u003e\u003cp\u003eYou will be given the perimeter P and the area A of a rectangle.  With these two values, calculate the area of the circle that circumscribes this rectangle.  This means we're looking for the area of the circle that touches this rectangle only at the four vertices of the rectangle.\u003c/p\u003e\u003cp\u003eGood luck, and Happy 2019!\u003c/p\u003e","function_template":"function y = wrecked_angles(P,A)\r\n  y = x;\r\nend","test_suite":"%%\r\nP=14;\r\nA=12;\r\ny=wrecked_angles(P,A);\r\ny_correct = 20.63495408493621;\r\njunk=abs(y-y_correct);\r\nassert(junk-1\u003c1e-10);\r\n%%\r\nP=34;\r\nA=60;\r\ny=wrecked_angles(P,A);\r\ny_correct = 131.7322896141688;\r\njunk=abs(y-y_correct);\r\nassert(junk-1\u003c1e-10);\r\n%%\r\nP=62;\r\nA=168;\r\ny=wrecked_angles(P,A);\r\ny_correct = 590.8738521234052;\r\njunk=abs(y-y_correct);\r\nassert(junk-100\u003c1e-10);\r\n%%\r\ns1=100;\r\ntotalsum=zeros(1,s1);\r\nfor s2=1:s1\r\n    P=2*(s1+s2);\r\n    A=s1*s2;\r\n    totalsum(s2)=wrecked_angles(P,A);\r\nend\r\ns=sum(totalsum);\r\ns_correct=1051137.631982975;\r\ns_junk=abs(s-s_correct);\r\nassert(s_junk\u003c1e-8);\r\n\r\nd=max(totalsum)-min(totalsum);\r\nd_correct=7853.196235811095;\r\nd_junk=abs(d-d_correct);\r\nassert(d_junk\u003c1e-8);\r\n%%\r\ns1=wrecked_angles(32,64);\r\ns2=wrecked_angles(72,288);\r\nP=2*(s1+s2);\r\nA=s1*s2;\r\ny=wrecked_angles(P,A);\r\ny_correct=259088.4479405854;\r\njunk=abs(y-y_correct);\r\nassert(junk\u003c1e-10);","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":72,"created_at":"2019-01-03T14:27:57.000Z","updated_at":"2026-05-30T01:37:57.000Z","published_at":"2019-01-03T14:27:57.000Z","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\u003eIt's time for some simple geometry fun to start off the new year.\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\u003eYou will be given the perimeter P and the area A of a rectangle. With these two values, calculate the area of the circle that circumscribes this rectangle. This means we're looking for the area of the circle that touches this rectangle only at the four vertices of the rectangle.\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\u003eGood luck, and Happy 2019!\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":61452,"title":"Geometry time 6!(Extremely hard)","description":"We have two circles. One small(C1) that is inside a bigger one (C2). C1 has a radius R1 and C2 has a radius R2. C1 is internally tangened to C2. On the perimeter of C1 lies a point (V). You are asked to find the coordinates of V(x,y) while C1 is moving alongside the perimeter of C2 without slipping.\r\n\r\nTip: Assume that the starting angle is at 0 degrees and that V is located at (-R1,0) at that angle.\r\nALSO KEEP IN MIND THAT: 'C1 MUST BE SMALLER THAN C2'.\r\nGOOD LUCK!!!!!!!!!!!!!!!!!!!!!!!!!!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 519.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 259.9px; transform-origin: 469px 259.9px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 31.5px; text-align: left; transform-origin: 445px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe have two circles. One small(C1) that is inside a bigger one (C2). C1 has a radius R1 and C2 has a radius R2. C1 is internally tangened to C2. On the perimeter of C1 lies a point (V). You are asked to find the coordinates of V(x,y) while C1 is moving alongside the perimeter of C2 without slipping.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 357.8px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 178.9px; text-align: left; transform-origin: 445px 178.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"376\" height=\"352\" style=\"vertical-align: baseline;width: 376px;height: 352px\" 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data-image-state=\"image-loaded\"\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eTip: Assume that the starting angle is at 0 degrees and that V is located at (-R1,0) at that angle.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eALSO KEEP IN MIND THAT: 'C1 MUST BE SMALLER THAN C2'.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [x,y] = find_coordinates(R1,R2,theta)\r\n     \r\nend","test_suite":"%% \r\nR1_test = randi([2, 15]);\r\nR2_test = R1_test + randi([1, 20]); \r\ntheta_test = 2 * pi * rand();\r\n[x_user, y_user] = find_coordinates(R1_test, R2_test, theta_test);\r\nd = R2_test - R1_test;\r\nA = [cos(theta_test), -sin(theta_test); sin(theta_test), cos(theta_test)];\r\nB = [cos((R2_test/R1_test)*theta_test), sin((R2_test/R1_test)*theta_test); ...\r\n    -sin((R2_test/R1_test)*theta_test), cos((R2_test/R1_test)*theta_test)];\r\nC_vec = A * [-d/sqrt(2); d/sqrt(2)];\r\nV_rel = B * [0; -R1_test];\r\nexpected = C_vec + V_rel;\r\ntol = 1e-5;\r\nassert(abs(x_user - expected(1)) \u003c tol \u0026\u0026 abs(y_user - expected(2)) \u003c tol, ...\r\n    'Test failed for R1 = %g, R2 = %g, theta = %g rad.', R1_test, R2_test, theta_test);\r\n%%\r\nR1_invalid = 10;\r\nR2_invalid = 9;\r\ntheta_dummy = 0;\r\ntry\r\n    find_coordinates(R1_invalid, R2_invalid, theta_dummy);\r\n    error('Test Failed: The function should have thrown an error when R1 \u003e R2.');\r\ncatch ME\r\n    expected_msg = 'C1 MUST BE SMALLER THAN C2';\r\n    assert(strcmp(ME.message, expected_msg), ...\r\n        'Test Failed: Error message was \"%s\" instead of \"%s\".', ME.message, expected_msg);\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":5158730,"edited_by":5158730,"edited_at":"2026-08-24T15:21:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-08-24T12:45:18.000Z","updated_at":"2026-08-26T15:39:43.000Z","published_at":"2026-08-24T12:45:18.000Z","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\u003eWe have two circles. One small(C1) that is inside a bigger one (C2). C1 has a radius R1 and C2 has a radius R2. C1 is internally tangened to C2. On the perimeter of C1 lies a point (V). You are asked to find the coordinates of V(x,y) while C1 is moving alongside the perimeter of C2 without slipping.\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=\\\"352\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"376\\\"/\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:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTip: Assume that the starting angle is at 0 degrees and that V is located at (-R1,0) at that angle.\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:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eALSO KEEP IN MIND THAT: 'C1 MUST BE SMALLER THAN C2'.\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\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!!!!!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60301,"title":"Compute the area of a lune","description":"Write a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius  of the smaller circle, the radius  of the larger circle, and the separation  between centers of the circles. \r\n","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: 405.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 202.85px; transform-origin: 407px 202.85px; 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-collapse: preserve; 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: 377.175px 8px; transform-origin: 377.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\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: 98.7917px 8px; transform-origin: 98.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the smaller circle, the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\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: 41.225px 8px; transform-origin: 41.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the larger circle, and the separation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\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: 98.4px 8px; transform-origin: 98.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e between centers of the circles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.7px; 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 166.85px; text-align: left; transform-origin: 384px 166.85px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = luneArea(a,b,c)\r\n%  a = radius of smaller circle\r\n%  b = radius of larger circle\r\n%  c = distance between the centers of the circles\r\n   y = (b-a)*(b+c)/2;\r\nend","test_suite":"%%\r\na = 1; \r\nb = 1.2;\r\nc = 0.9; \r\nA = luneArea(a,b,c);\r\nA_correct = 1.285341014608472;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = 4; \r\nb = 5;\r\nc = 3; \r\nA = luneArea(a,b,c);\r\nA_correct = 13.950360778678039;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = exp(1); \r\nb = pi;\r\nc = -psi(1); \r\nA = luneArea(a,b,c);\r\nA_correct = 0.443456401155954;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = 3; \r\nb = 4;\r\nc = 1.01; \r\nA = luneArea(a,b,c);\r\nA_correct = 0.0065019633283;\r\nassert(abs(A-A_correct)/A_correct\u003c8e-12)\r\n\r\n%%\r\na = 1/sqrt(2); \r\nb = 1;\r\nc = a; \r\nA = luneArea(a,b,c);\r\nA_correct = 1/2;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%% \r\na = 5*rand;\r\nb = a*sqrt(2);\r\nc = a; \r\nA = luneArea(a,b,c);\r\nA_correct = b^2/2;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-01T23:28:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2024-06-01T23:28:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-13T12:25:08.000Z","updated_at":"2026-06-05T04:53:03.000Z","published_at":"2024-05-13T12:25:26.000Z","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\u003eWrite a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius \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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the smaller circle, the radius \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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the larger circle, and the separation \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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e between centers of the circles. \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=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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time3!(Medium)","description":"This time we have two circles! The shape is given below:\r\n\r\nYou are requested to calculate the area of the two circles(A1 ,A2) given the distance O1O2 = a, the distance D and that both the angle O1AB and O2BA are 90 degrees.\r\nExplanation(if needed):O1O2 is the line that connects the centers of both circles.\r\nTips:1) You can draw a line somewhere on this shape if you want.\r\n2) The circles are tangent.\r\nGOOD LUCK!!!!!!!!!!!!!!!!!!!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 407.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 203.9px; transform-origin: 469px 203.9px; vertical-align: baseline; \"\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis time we have two circles! The shape is given below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 206.8px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 103.4px; text-align: left; transform-origin: 445px 103.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"309\" height=\"201\" style=\"vertical-align: baseline;width: 309px;height: 201px\" 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\" data-image-state=\"image-loaded\"\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are requested to calculate the area of the two circles(A1 ,A2) given the distance O1O2 = a, the distance D and that both the angle O1AB and O2BA are 90 degrees.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eExplanation(if needed):O1O2 is the line that connects the centers of both circles.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eTips:1) You can draw a line somewhere on this shape if you want.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003e2) The circles are tangent.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [A1,A2] = find_the_circles_area(a,D)\r\n  \r\nend","test_suite":"%%\r\na = 7;\r\nD = 6;\r\nA1_exp = (pi*(7 + sqrt(13))^2)/4;\r\nA2_exp = (pi*(7 - sqrt(13))^2)/4;\r\n[A1_act, A2_act] = find_the_circles_area(a, D);\r\nassert(abs(A1_act - A1_exp) \u003c 1e-4, 'A1 is wrong.');\r\nassert(abs(A2_act - A2_exp) \u003c 1e-4, 'A2 is wrong.');\r\n%%\r\nD_val = randi([5, 50]);\r\na_val = D_val + randi([1, 20]);\r\nd = sort(roots([1, -2*a_val, D_val^2]), 'descend');\r\nA1_ref = (pi/4) * d(1)^2;\r\nA2_ref = (pi/4) * d(2)^2;\r\n[A1_user, A2_user] = find_the_circles_area(a_val, D_val);\r\nassert(abs(A1_user - A1_ref) \u003c 1e-4, 'A1 is wrong.');\r\nassert(abs(A2_user - A2_ref) \u003c 1e-4, 'A2 is wrong.');","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5158730,"edited_by":5158730,"edited_at":"2026-08-23T22:22:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-08-23T22:20:50.000Z","updated_at":"2026-08-27T13:35:31.000Z","published_at":"2026-08-23T22:20:50.000Z","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\u003eThis time we have two circles! The shape is given below:\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=\\\"201\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"309\\\"/\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\u003eYou are requested to calculate the area of the two circles(A1 ,A2) given the distance O1O2 = a, the distance D and that both the angle O1AB and O2BA are 90 degrees.\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:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation(if needed):O1O2 is the line that connects the centers of both circles.\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:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTips:1) You can draw a line somewhere on this shape if you want.\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:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2) The circles are 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44817,"title":"Wrecked Angles?","description":"It's time for some simple geometry fun to start off the new year.\r\n\r\nYou will be given the perimeter P and the area A of a rectangle.  With these two values, calculate the area of the circle that circumscribes this rectangle.  This means we're looking for the area of the circle that touches this rectangle only at the four vertices of the rectangle.\r\n\r\nGood luck, and Happy 2019!","description_html":"\u003cp\u003eIt's time for some simple geometry fun to start off the new year.\u003c/p\u003e\u003cp\u003eYou will be given the perimeter P and the area A of a rectangle.  With these two values, calculate the area of the circle that circumscribes this rectangle.  This means we're looking for the area of the circle that touches this rectangle only at the four vertices of the rectangle.\u003c/p\u003e\u003cp\u003eGood luck, and Happy 2019!\u003c/p\u003e","function_template":"function y = wrecked_angles(P,A)\r\n  y = x;\r\nend","test_suite":"%%\r\nP=14;\r\nA=12;\r\ny=wrecked_angles(P,A);\r\ny_correct = 20.63495408493621;\r\njunk=abs(y-y_correct);\r\nassert(junk-1\u003c1e-10);\r\n%%\r\nP=34;\r\nA=60;\r\ny=wrecked_angles(P,A);\r\ny_correct = 131.7322896141688;\r\njunk=abs(y-y_correct);\r\nassert(junk-1\u003c1e-10);\r\n%%\r\nP=62;\r\nA=168;\r\ny=wrecked_angles(P,A);\r\ny_correct = 590.8738521234052;\r\njunk=abs(y-y_correct);\r\nassert(junk-100\u003c1e-10);\r\n%%\r\ns1=100;\r\ntotalsum=zeros(1,s1);\r\nfor s2=1:s1\r\n    P=2*(s1+s2);\r\n    A=s1*s2;\r\n    totalsum(s2)=wrecked_angles(P,A);\r\nend\r\ns=sum(totalsum);\r\ns_correct=1051137.631982975;\r\ns_junk=abs(s-s_correct);\r\nassert(s_junk\u003c1e-8);\r\n\r\nd=max(totalsum)-min(totalsum);\r\nd_correct=7853.196235811095;\r\nd_junk=abs(d-d_correct);\r\nassert(d_junk\u003c1e-8);\r\n%%\r\ns1=wrecked_angles(32,64);\r\ns2=wrecked_angles(72,288);\r\nP=2*(s1+s2);\r\nA=s1*s2;\r\ny=wrecked_angles(P,A);\r\ny_correct=259088.4479405854;\r\njunk=abs(y-y_correct);\r\nassert(junk\u003c1e-10);","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":72,"created_at":"2019-01-03T14:27:57.000Z","updated_at":"2026-05-30T01:37:57.000Z","published_at":"2019-01-03T14:27:57.000Z","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\u003eIt's time for some simple geometry fun to start off the new year.\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\u003eYou will be given the perimeter P and the area A of a rectangle. With these two values, calculate the area of the circle that circumscribes this rectangle. This means we're looking for the area of the circle that touches this rectangle only at the four vertices of the rectangle.\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\u003eGood luck, and Happy 2019!\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":61452,"title":"Geometry time 6!(Extremely hard)","description":"We have two circles. One small(C1) that is inside a bigger one (C2). C1 has a radius R1 and C2 has a radius R2. C1 is internally tangened to C2. On the perimeter of C1 lies a point (V). You are asked to find the coordinates of V(x,y) while C1 is moving alongside the perimeter of C2 without slipping.\r\n\r\nTip: Assume that the starting angle is at 0 degrees and that V is located at (-R1,0) at that angle.\r\nALSO KEEP IN MIND THAT: 'C1 MUST BE SMALLER THAN C2'.\r\nGOOD LUCK!!!!!!!!!!!!!!!!!!!!!!!!!!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 519.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 259.9px; transform-origin: 469px 259.9px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 31.5px; text-align: left; transform-origin: 445px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe have two circles. One small(C1) that is inside a bigger one (C2). C1 has a radius R1 and C2 has a radius R2. C1 is internally tangened to C2. On the perimeter of C1 lies a point (V). You are asked to find the coordinates of V(x,y) while C1 is moving alongside the perimeter of C2 without slipping.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 357.8px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 178.9px; text-align: left; transform-origin: 445px 178.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"376\" height=\"352\" style=\"vertical-align: baseline;width: 376px;height: 352px\" 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data-image-state=\"image-loaded\"\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eTip: Assume that the starting angle is at 0 degrees and that V is located at (-R1,0) at that angle.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eALSO KEEP IN MIND THAT: 'C1 MUST BE SMALLER THAN C2'.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [x,y] = find_coordinates(R1,R2,theta)\r\n     \r\nend","test_suite":"%% \r\nR1_test = randi([2, 15]);\r\nR2_test = R1_test + randi([1, 20]); \r\ntheta_test = 2 * pi * rand();\r\n[x_user, y_user] = find_coordinates(R1_test, R2_test, theta_test);\r\nd = R2_test - R1_test;\r\nA = [cos(theta_test), -sin(theta_test); sin(theta_test), cos(theta_test)];\r\nB = [cos((R2_test/R1_test)*theta_test), sin((R2_test/R1_test)*theta_test); ...\r\n    -sin((R2_test/R1_test)*theta_test), cos((R2_test/R1_test)*theta_test)];\r\nC_vec = A * [-d/sqrt(2); d/sqrt(2)];\r\nV_rel = B * [0; -R1_test];\r\nexpected = C_vec + V_rel;\r\ntol = 1e-5;\r\nassert(abs(x_user - expected(1)) \u003c tol \u0026\u0026 abs(y_user - expected(2)) \u003c tol, ...\r\n    'Test failed for R1 = %g, R2 = %g, theta = %g rad.', R1_test, R2_test, theta_test);\r\n%%\r\nR1_invalid = 10;\r\nR2_invalid = 9;\r\ntheta_dummy = 0;\r\ntry\r\n    find_coordinates(R1_invalid, R2_invalid, theta_dummy);\r\n    error('Test Failed: The function should have thrown an error when R1 \u003e R2.');\r\ncatch ME\r\n    expected_msg = 'C1 MUST BE SMALLER THAN C2';\r\n    assert(strcmp(ME.message, expected_msg), ...\r\n        'Test Failed: Error message was \"%s\" instead of \"%s\".', ME.message, expected_msg);\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":5158730,"edited_by":5158730,"edited_at":"2026-08-24T15:21:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-08-24T12:45:18.000Z","updated_at":"2026-08-26T15:39:43.000Z","published_at":"2026-08-24T12:45:18.000Z","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\u003eWe have two circles. One small(C1) that is inside a bigger one (C2). C1 has a radius R1 and C2 has a radius R2. C1 is internally tangened to C2. On the perimeter of C1 lies a point (V). You are asked to find the coordinates of V(x,y) while C1 is moving alongside the perimeter of C2 without slipping.\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=\\\"352\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"376\\\"/\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:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTip: Assume that the starting angle is at 0 degrees and that V is located at (-R1,0) at that angle.\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:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eALSO KEEP IN MIND THAT: 'C1 MUST BE SMALLER THAN C2'.\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\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!!!!!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60301,"title":"Compute the area of a lune","description":"Write a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius  of the smaller circle, the radius  of the larger circle, and the separation  between centers of the circles. \r\n","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: 405.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 202.85px; transform-origin: 407px 202.85px; 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-collapse: preserve; 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: 377.175px 8px; transform-origin: 377.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\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: 98.7917px 8px; transform-origin: 98.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the smaller circle, the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\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: 41.225px 8px; transform-origin: 41.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the larger circle, and the separation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\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: 98.4px 8px; transform-origin: 98.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e between centers of the circles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.7px; 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 166.85px; text-align: left; transform-origin: 384px 166.85px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = luneArea(a,b,c)\r\n%  a = radius of smaller circle\r\n%  b = radius of larger circle\r\n%  c = distance between the centers of the circles\r\n   y = (b-a)*(b+c)/2;\r\nend","test_suite":"%%\r\na = 1; \r\nb = 1.2;\r\nc = 0.9; \r\nA = luneArea(a,b,c);\r\nA_correct = 1.285341014608472;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = 4; \r\nb = 5;\r\nc = 3; \r\nA = luneArea(a,b,c);\r\nA_correct = 13.950360778678039;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = exp(1); \r\nb = pi;\r\nc = -psi(1); \r\nA = luneArea(a,b,c);\r\nA_correct = 0.443456401155954;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = 3; \r\nb = 4;\r\nc = 1.01; \r\nA = luneArea(a,b,c);\r\nA_correct = 0.0065019633283;\r\nassert(abs(A-A_correct)/A_correct\u003c8e-12)\r\n\r\n%%\r\na = 1/sqrt(2); \r\nb = 1;\r\nc = a; \r\nA = luneArea(a,b,c);\r\nA_correct = 1/2;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%% \r\na = 5*rand;\r\nb = a*sqrt(2);\r\nc = a; \r\nA = luneArea(a,b,c);\r\nA_correct = b^2/2;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-01T23:28:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2024-06-01T23:28:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-13T12:25:08.000Z","updated_at":"2026-06-05T04:53:03.000Z","published_at":"2024-05-13T12:25:26.000Z","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\u003eWrite a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius \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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the smaller circle, the radius \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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the larger circle, and the separation \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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e between centers of the circles. \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=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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