{"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":"ee379031-8feb-534d-80f7-f1c3ff8e78e0","task_key":"geometry--test--ee379031-8feb-534d-80f7-f1c3ff8e78e0","task_revision_id":"1","upstream_id":"","short_description":"Three semicircles of radius 1 are constructed on diameter $\\overline{AB}$ of a…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Three semicircles of radius 1 are constructed on diameter $\\\\overline{AB}$ of a semicircle of radius 2. The centers of the small semicircles divide $\\\\overline{AB}$  into four line segments of equal length, as shown. What is the area of the shaded region that lies  within the large semicircle but outside the smaller semicircles? Express your answer in terms of $\\\\pi$ and in simplest radical form.\\n\\n[asy]\\nfill((0,2)..(2,0)--(-2,0)..cycle,gray(0.7));\\nfill((-1,1)..(0,0)--(-2,0)..cycle,white);\\nfill((1,1)..(0,0)--(2,0)..cycle,white);\\nfill((0,1)..(1,0)--(-1,0)..cycle,white);\\ndraw((0,1)..(1,0)--(-1,0)..cycle,dashed);\\ndraw((0,2)..(2,0)--(-2,0)..cycle);\\nlabel(\\\"$A$\\\",(-2,0),W);\\nlabel(\\\"$B$\\\",(2,0),E);\\nlabel(\\\"1\\\",(-1.5,0),S);\\nlabel(\\\"2\\\",(0,0),S);\\nlabel(\\\"1\\\",(1.5,0),S);\\ndot((0,0));\\ndot((-1,0));\\ndot((1,0));\\ndraw((-2,-0.1)--(-2,-0.4));\\ndraw((-1,-0.1)--(-1,-0.4));\\ndraw((2,-0.1)--(2,-0.4));\\ndraw((1,-0.1)--(1,-0.4));\\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":[]}