{"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":"9443d867-1f9e-5a1b-ae21-172427252308","task_key":"precalculus--test--9443d867-1f9e-5a1b-ae21-172427252308","task_revision_id":"1","upstream_id":"","short_description":"Triangle $ABC$ is isosceles, with $AB=AC$ and altitude $AM=11.$ Suppose that…","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Triangle $ABC$ is isosceles, with $AB=AC$ and altitude $AM=11.$ Suppose that there is a point $D$ on $\\\\overline{AM}$ with $AD=10$ and $\\\\angle BDC=3\\\\angle BAC.$  Find the perimeter of triangle $ABC.$\\n\\n[asy]\\nunitsize(0.4 cm);\\n\\npair A, B, C, D, M;\\n\\nA = (0,11);\\nD = (0,1);\\nB = (-11/2,0);\\nC = (11/2,0);\\nM = (B + C)/2;\\n\\ndraw(A--B--C--cycle);\\ndraw(A--M);\\ndraw(B--D--C);\\n\\nlabel(\\\"$A$\\\", A, N);\\nlabel(\\\"$B$\\\", B, SW);\\nlabel(\\\"$C$\\\", C, SE);\\nlabel(\\\"$D$\\\", D, NW);\\nlabel(\\\"$M$\\\", M, S);\\n[/asy]\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}