{"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":"451d8e53-2164-5821-9d48-3df3f166d3b1","task_key":"geometry--test--451d8e53-2164-5821-9d48-3df3f166d3b1","task_revision_id":"1","upstream_id":"","short_description":"In triangle $ABC$, $AB = AC = 5$ and $BC = 6$. Let $O$ be the circumcenter of…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In triangle $ABC$, $AB = AC = 5$ and $BC = 6$.  Let $O$ be the circumcenter of triangle $ABC$.  Find the area of triangle $OBC$.\\n\\n[asy]\\nunitsize(0.6 cm);\\n\\npair A, B, C, O;\\n\\nA = (0,4);\\nB = (-3,0);\\nC = (3,0);\\nO = circumcenter(A,B,C);\\n\\ndraw(A--B--C--cycle);\\ndraw(circumcircle(A,B,C));\\ndraw(B--O--C);\\n\\nlabel(\\\"$A$\\\", A, N);\\nlabel(\\\"$B$\\\", B, SW);\\nlabel(\\\"$C$\\\", C, SE);\\nlabel(\\\"$O$\\\", O, N);\\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":[]}