{"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":"2cfade28-0c92-5e8d-aba6-095fa557c649","task_key":"geometry--test--2cfade28-0c92-5e8d-aba6-095fa557c649","task_revision_id":"1","upstream_id":"","short_description":"In the diagram, two circles, each with center $D$, have radii of $1$ and $2$.…","config":"geometry","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"In the diagram, two circles, each with center $D$, have radii of $1$ and $2$. The total area of the shaded region is $\\\\frac5{12}$ of the area of the larger circle. How many degrees are in the measure of (the smaller) $\\\\angle ADC$?\\n[asy]\\nsize(4cm);\\ndefaultpen(linewidth(0.75));\\nreal adc = 100;\\npair d = (0, 0); pair a = 2 * dir(100); pair c = (2, 0);\\npath inner = arc(d, a/2, c/2, CW);\\n\\npath outer = arc(d, c, a, CCW);\\nguide region1 = (a--a/2)..inner..(c/2--c)..outer..cycle;\\nguide region2 = arc(d, a/2, c/2, CCW)..(c/2--d--a/2)..cycle;\\nfill(region1, gray(0.75));\\nfill(region2, gray(0.75));\\ndraw(unitcircle); draw(scale(2) * unitcircle);\\ndraw(a--d--c);\\nlabel(\\\"$A$\\\", a, N); label(\\\"$C$\\\", c, E); label(\\\"$D$\\\", d, NE);\\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":[]}