{"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":"d7fee75c-e2e3-5c30-b916-ed909b27975a","task_key":"geometry--test--d7fee75c-e2e3-5c30-b916-ed909b27975a","task_revision_id":"1","upstream_id":"","short_description":"Distinct points $A$ and $B$ are on a semicircle with diameter $MN$ and center…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Distinct points $A$ and $B$ are on a semicircle with diameter $MN$ and center $C$.  The point $P$ is on $CN$ and $\\\\angle CAP = \\\\angle CBP = 10^\\\\circ$.  If arc $MA$ is equal to $40^\\\\circ$, then find arc $BN$ (in degrees).\\n\\n[asy]\\nimport geometry;\\nimport graph;\\n\\nunitsize(2 cm);\\n\\npair A, B, C, M, N, P;\\n\\nM = (-1,0);\\nN = (1,0);\\nC = (0,0);\\nA = dir(140);\\nB = dir(20);\\nP = extension(A, A + rotate(10)*(C - A), B, B + rotate(10)*(C - B));\\n\\ndraw(M--N);\\ndraw(arc(C,1,0,180));\\ndraw(A--C--B);\\ndraw(A--P--B);\\n\\nlabel(\\\"$A$\\\", A, NW);\\nlabel(\\\"$B$\\\", B, NE);\\nlabel(\\\"$C$\\\", C, S);\\nlabel(\\\"$M$\\\", M, SW);\\nlabel(\\\"$N$\\\", N, SE);\\nlabel(\\\"$P$\\\", P, 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":[]}