{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"92b9e004-1256-51e3-b2b1-bf23cfc7c602","task_key":"geometry--test--92b9e004-1256-51e3-b2b1-bf23cfc7c602","task_revision_id":"1","upstream_id":"","short_description":"Given regular pentagon $ABCDE,$ a circle can be drawn that is tangent to…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Given regular pentagon $ABCDE,$ a circle can be drawn that is tangent to $\\\\overline{DC}$ at $D$ and to $\\\\overline{AB}$ at $A.$ In degrees, what is the measure of minor arc $AD$? [asy]import olympiad; import geometry; size(100); defaultpen(linewidth(0.8));\\npair[] pentagon = new pair[5];\\npentagon[0] = dir(36);\\npentagon.cyclic=true;\\nfor(int i = 1; i < 6; ++i){\\n \\npentagon[i] = dir(72*i + 36);\\n\\ndraw(pentagon[i - 1]--pentagon[i]);\\n}\\ndot(\\\"$C$\\\",pentagon[0],NE);\\ndot(\\\"$D$\\\",pentagon[1],N);\\ndot(\\\"$E$\\\",pentagon[2],W);\\ndot(\\\"$A$\\\",pentagon[3],S);\\ndot(\\\"$B$\\\",pentagon[4],SE);\\nline x = line(pentagon[1],pentagon[1] + dir(-108));\\nline x2 = line(origin,pentagon[2]);\\npair ccenter = coordinates(intersectionpoint(x,x2));\\ndraw(Circle(ccenter,arclength(ccenter--pentagon[1])));\\n[/asy]\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}