{"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":"14b823de-c29c-53dd-8516-2764bb36f9aa","task_key":"precalculus--test--14b823de-c29c-53dd-8516-2764bb36f9aa","task_revision_id":"1","upstream_id":"","short_description":"Given triangle $ABC,$ there exists a unique point $P$ such that","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Given triangle $ABC,$ there exists a unique point $P$ such that\\n\\\\[AB^2 + AP^2 + BP^2 = AC^2 + AP^2 + CP^2 = BC^2 + BP^2 + CP^2.\\\\]Express the common value above in terms of the side lengths $a,$ $b,$ and $c,$ and circumradius $R$ of triangle $ABC.$\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}