{"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":"63d3f809-5a29-5c4f-8b1b-19fded553a9d","task_key":"intermediate~5falgebra--test--63d3f809-5a29-5c4f-8b1b-19fded553a9d","task_revision_id":"1","upstream_id":"","short_description":"Three noncollinear points and a line $\\ell$ are given in the plane. Suppose no…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Three noncollinear points and a line $\\\\ell$ are given in the plane. Suppose no two of the points lie on a line parallel to $\\\\ell$ (or $\\\\ell$ itself). There are exactly $n$ lines $m$ perpendicular to $\\\\ell$ with the following property: the three circles with centers at the given points and tangent to line $m$ all concur at some point. Find all possible values of $n$.\\n\\nEnter all possible values of $n,$ separated by commas.\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}