{"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":"0d082a38-7cfb-510c-a010-6afead276a23","task_key":"geometry--test--0d082a38-7cfb-510c-a010-6afead276a23","task_revision_id":"1","upstream_id":"","short_description":"Isosceles right triangle $ABC$ encloses a semicircle of area $2\\pi$. The circle…","config":"geometry","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"Isosceles right triangle $ABC$ encloses a semicircle of area $2\\\\pi$. The circle has its center $O$ on hypotenuse $\\\\overline{AB}$ and is tangent to sides $\\\\overline{AC}$ and $\\\\overline{BC}$. What is the area of triangle $ABC$? [asy]\\npair a=(4,4), b=(0,0), c=(0,4), d=(4,0), o=(2,2);\\ndraw(circle(o, 2));\\nclip(a--b--c--cycle);\\ndraw(a--b--c--cycle);\\ndot(o);\\nlabel(\\\"$C$\\\", c, NW);\\nlabel(\\\"$A$\\\", a, NE);\\nlabel(\\\"$B$\\\", b, SW);\\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":[]}