{"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":"64c511f1-4f26-5100-94e0-eb0b46de03b9","task_key":"geometry--test--64c511f1-4f26-5100-94e0-eb0b46de03b9","task_revision_id":"1","upstream_id":"","short_description":"What is the ratio of the area of triangle $BDC$ to the area of triangle $ADC$?…","config":"geometry","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"What is the ratio of the area of triangle $BDC$ to the area of triangle $ADC$? Express your answer as a common fraction.\\n\\n[asy]\\ndraw((0,0)--(10sqrt(3),0)--(0,10)--(0,0)--cycle,linewidth(2));\\ndraw(5sqrt(3)*dir(60)--(0,0),linewidth(2));\\n\\ndraw((1,0)--(1,1)--(0,1),linewidth(1));\\ndraw(5sqrt(3)*dir(60)+1*dir(-120)--(5sqrt(3)-1)*dir(60)+1*dir(-30)--5sqrt(3)*dir(60)+1*dir(-30),linewidth(1));\\n\\nlabel(\\\"A\\\",(10sqrt(3),0),E);\\nlabel(\\\"B\\\",(0,10),W);\\nlabel(\\\"C\\\",(0,0),SW);\\nlabel(\\\"D\\\",5sqrt(3)*dir(60),NE);\\nlabel(\\\"$30^{\\\\circ}$\\\",(12,0),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":[]}