{"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":"a50c368b-325f-58d4-a878-fd4c510281ce","task_key":"geometry--test--a50c368b-325f-58d4-a878-fd4c510281ce","task_revision_id":"1","upstream_id":"","short_description":"A unit circle has its center at $(5,0)$ and a second circle with a radius of $2$…","config":"geometry","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"A unit circle has its center at $(5,0)$ and a second circle with a radius of $2$ units has its center at $(11,0)$ as shown. A common internal tangent to the circles intersects the $x$-axis at $Q(a,0)$. What is the value of $a$? [asy]\\ndraw((-2,0)--(15,0),Arrows);\\ndraw((0,-4)--(0,5),Arrows);\\ndraw(Circle((5,0),1));\\ndraw(Circle((11,0),2));\\ndot((5,0));\\ndot((7,0));\\ndot((11,0));\\nlabel(scale(0.7)*Label(\\\"(5,0)\\\",(3,0),S));\\nlabel(\\\"Q\\\",(7,0),N);\\nlabel(scale(0.7)*Label(\\\"(11,0)\\\",(11,0),S));\\nlabel(\\\"$x$\\\",(15,0),S);\\nlabel(\\\"$y$\\\",(0,5),W);\\ndraw((1,3.46410162)--(14,-4.04145188),Arrows);\\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":[]}