{"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":"66e225c5-cfcd-5910-8fb6-d36a772aec92","task_key":"geometry--test--66e225c5-cfcd-5910-8fb6-d36a772aec92","task_revision_id":"1","upstream_id":"","short_description":"Three congruent isosceles triangles $DAO,$ $AOB,$ and $OBC$ have…","config":"geometry","split":"test","body":"{\"level\":\"Level 2\",\"problem\":\"Three congruent isosceles triangles $DAO,$ $AOB,$ and $OBC$ have $AD=AO=OB=BC=10$ and $AB=DO=OC=12.$ These triangles are arranged to form trapezoid $ABCD,$ as shown. Point $P$ is on side $AB$ so that $OP$ is perpendicular to $AB.$ [asy]\\npair A, B, C, D, O, P;\\nA= (6, 8);\\nB=(18, 8);\\nC=(24, 0);\\nD=(0,0);\\nO=(12,0);\\nP=(12,8);\\ndraw(A--B--C--D--A);\\ndraw(A--O--B);\\ndraw(O--P, dashed);\\nlabel(\\\"A\\\", A, NW);\\nlabel(\\\"B\\\", B, NE);\\nlabel(\\\"C\\\", C, SE);\\nlabel(\\\"D\\\", D, SW);\\nlabel(\\\"O\\\", O, S);\\nlabel(\\\"P\\\", P, N);\\nlabel(\\\"12\\\", (D+O)/2, S);\\nlabel(\\\"12\\\", (O+C)/2, S);\\nlabel(\\\"10\\\", (A+D)/2, NW);\\nlabel(\\\"10\\\", (B+C)/2, NE);\\n[/asy] What is the length of $OP?$\",\"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":[]}