{"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":"4e069a28-a5d3-5528-be4f-faf1667bfe5f","task_key":"geometry--test--4e069a28-a5d3-5528-be4f-faf1667bfe5f","task_revision_id":"1","upstream_id":"","short_description":"Four circles of radius 1 are each tangent to two sides of a square and…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Four circles of radius 1 are each tangent to two sides of a square and externally tangent to a circle of radius 2, as shown.  What is the area of the square?\\n\\n[asy]\\nunitsize(1cm);draw(Circle((0,0),2));\\nfor(int i=0; i<4; ++i) {\\n\\tdraw(Circle(scale(3)*dir(45+90*i),1));\\n\\tdraw((3+sqrt(2))*dir(45+90*i)--(3+sqrt(2))*dir(-45+90*i));  \\n}\\ndraw((0,0)--(2,0));\\nlabel(\\\"2\\\",(1,0),N);\\ndraw(scale(3)*dir(45+90*1)--shift((1,0))*scale(3)*dir(45+90*1));\\nlabel(\\\"1\\\",point(scale(3)*dir(45+90*1)--shift((1,0))*scale(3)*dir(45+90*1),.5),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":[]}