{"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":"131dba59-f88c-5736-bbbe-550bd1e3a76a","task_key":"geometry--test--131dba59-f88c-5736-bbbe-550bd1e3a76a","task_revision_id":"1","upstream_id":"","short_description":"In acute triangle $ABC$, altitudes $AD$, $BE$, and $CF$ intersect at the…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In acute triangle $ABC$, altitudes $AD$, $BE$, and $CF$ intersect at the orthocenter $H$.  If $BD = 5$, $CD = 9$, and $CE = 42/5$, then find the length of $HE$.\\n\\n[asy]\\nunitsize(0.3 cm);\\n\\npair A, B, C, D, E, F, H;\\n\\nA = (5,12);\\nB = (0,0);\\nC = (14,0);\\nD = (A + reflect(B,C)*(A))/2;\\nE = (B + reflect(C,A)*(B))/2;\\nF = (C + reflect(A,B)*(C))/2;\\nH = extension(B,E,C,F);\\n\\ndraw(A--B--C--cycle);\\ndraw(A--D);\\ndraw(B--E);\\ndraw(C--F);\\n\\nlabel(\\\"$A$\\\", A, N);\\nlabel(\\\"$B$\\\", B, SW);\\nlabel(\\\"$C$\\\", C, SE);\\nlabel(\\\"$D$\\\", D, S);\\nlabel(\\\"$E$\\\", E, NE);\\nlabel(\\\"$F$\\\", F, NW);\\nlabel(\\\"$H$\\\", H, SE);\\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":[]}