{"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":"875bc345-b0d0-507b-a27e-e88b3d4a2461","task_key":"geometry--test--875bc345-b0d0-507b-a27e-e88b3d4a2461","task_revision_id":"1","upstream_id":"","short_description":"Isosceles $\\triangle{ABC}$ has a right angle at $C$. Point $P$ is inside…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Isosceles $\\\\triangle{ABC}$ has a right angle at $C$.  Point $P$ is inside $\\\\triangle{ABC}$, such that $PA=11$, $PB=7$, and $PC=6$. Legs $\\\\overline{AC}$ and $\\\\overline{BC}$ have length $s=\\\\sqrt{a+b\\\\sqrt{2}}$, where $a$ and $b$ are positive integers. What is $a+b$?\\n\\n[asy]\\npair A,B,C,P;\\nA=(10,0);\\nB=(0,10);\\nC=(0,0);\\nP=(3,3.5);\\ndraw(A--B--C--cycle,linewidth(0.7));\\ndraw(A--P,linewidth(0.7));\\ndraw(B--P--C,linewidth(0.7));\\nlabel(\\\"$A$\\\",A,E);\\nlabel(\\\"$B$\\\",B,N);\\nlabel(\\\"$C$\\\",C,S);\\nlabel(\\\"$P$\\\",P,NE);\\nlabel(\\\"7\\\",(1.5,6.75),E);\\nlabel(\\\"6\\\",(1.5, 1.75),E);\\nlabel(\\\"11\\\",(6.5,1.75),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":[]}