{"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":"8179e6a1-1a6d-59ee-825a-64a93d613e0b","task_key":"geometry--test--8179e6a1-1a6d-59ee-825a-64a93d613e0b","task_revision_id":"1","upstream_id":"","short_description":"Two parallel chords in a circle have lengths 10 and 14, and the distance between…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Two parallel chords in a circle have lengths 10 and 14, and the distance between them is 6. The chord parallel to these chords and midway between them is of length $\\\\sqrt{a}$. Find the value of $a$. [asy]\\nimport olympiad; import geometry; size(100); defaultpen(linewidth(0.8));\\ndraw(unitcircle);\\ndraw(Label(\\\"14\\\",align=N),dir(30)--dir(150));\\ndraw(Label(\\\"10\\\",align=N),dir(-40)--dir(-140));\\ndraw(Label(\\\"$\\\\sqrt{a}$\\\",align=N),dir(-5)--dir(-175));\\ndistance(rotate(90)*\\\"6\\\",(1,Sin(30)),(1,Sin(-40)),-9,Arrows(size=1));\\n\\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":[]}