{"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":"ba47e3a6-548e-52c0-98c0-a815895cbe38","task_key":"geometry--test--ba47e3a6-548e-52c0-98c0-a815895cbe38","task_revision_id":"1","upstream_id":"","short_description":"Triangles $ABC$ and $ABD$ are isosceles with $AB=AC=BD$, and $\\overline{BD}$…","config":"geometry","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Triangles $ABC$ and $ABD$ are  isosceles with $AB=AC=BD$, and $\\\\overline{BD}$ intersects $\\\\overline{AC}$ at $E$. If $\\\\overline{BD}\\\\perp\\\\overline{AC}$, then what is the value of $\\\\angle C+\\\\angle D$? [asy]\\nimport olympiad; import geometry; size(150); defaultpen(linewidth(0.8));\\ndraw(origin--(dir(70))--(2*Cos(70),0)--cycle);\\ndraw(origin--(dir(20))--(dir(70))--cycle);\\npair E = intersectionpoint(origin--dir(20),dir(70)--(2*Cos(70),0));\\ndot(\\\"$E$\\\",E);\\npair A = dir(70);\\npair B = origin;\\npair C = (2*Cos(70),0);\\npair D = dir(20);\\ndot(\\\"$A$\\\",A,N);\\ndot(\\\"$B$\\\",B,SW);\\ndot(\\\"$C$\\\",C,SE);\\ndot(\\\"$D$\\\",D,E);\\ndraw(rightanglemark(B,E,A,1.5));\\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":[]}