{"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":"26c9fa97-f1fc-5b9c-84d2-cdca81649f59","task_key":"geometry--test--26c9fa97-f1fc-5b9c-84d2-cdca81649f59","task_revision_id":"1","upstream_id":"","short_description":"In triangle $ABC$, $AB = 13$, $AC = 15$, and $BC = 14$. Let $I$ be the incenter.…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In triangle $ABC$, $AB = 13$, $AC = 15$, and $BC = 14$.  Let $I$ be the incenter.  The incircle of triangle $ABC$ touches sides $BC$, $AC$, and $AB$ at $D$, $E$, and $F$, respectively.  Find the area of quadrilateral $AEIF$.\\n\\n[asy]\\nimport geometry;\\n\\nunitsize(2 cm);\\n\\npair A, B, C, D, E, F, I;\\n\\nA = (1,2);\\nB = (0,0);\\nC = (3,0);\\nI = incenter(A,B,C);\\nD = (I + reflect(B,C)*(I))/2;\\nE = (I + reflect(C,A)*(I))/2;\\nF = (I + reflect(A,B)*(I))/2;\\n\\ndraw(A--B--C--cycle);\\ndraw(incircle(A,B,C));\\ndraw(E--I--F);\\n\\nlabel(\\\"$A$\\\", A, N);\\nlabel(\\\"$B$\\\", B, SW);\\nlabel(\\\"$C$\\\", C, SE);\\nlabel(\\\"$D$\\\", D, S);\\nlabel(\\\"$E$\\\", E, NE);\\nlabel(\\\"$F$\\\", F, NW);\\nlabel(\\\"$I$\\\", I, S);\\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":[]}