{"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":"161e0c28-f0c2-528b-ab39-a5fecdd34b0d","task_key":"geometry--test--161e0c28-f0c2-528b-ab39-a5fecdd34b0d","task_revision_id":"1","upstream_id":"","short_description":"Three circles of radius $s$ are drawn in the first quadrant of the $xy$-plane.…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Three circles of radius $s$ are drawn in the first quadrant of the $xy$-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the $x$-axis, and the third is tangent to the first circle and the $y$-axis. A circle of radius $r>s$ is tangent to both axes and to the second and third circles. What is $r/s$?\\n\\n[asy]\\ndraw((0,25)--(0,0)--(25,0),linewidth(0.7));\\ndraw(Circle((1,1),1),linewidth(0.7));\\ndraw(Circle((3,1),1),linewidth(0.7));\\ndraw(Circle((1,3),1),linewidth(0.7));\\ndraw(Circle((9,9),9),linewidth(0.7));\\ndraw((1,3)--(1,4),dashed);\\ndraw((9,9)--(9,0),dashed);\\ndraw((-1,3.5)--(1,3.5),dashed);\\nlabel(\\\"$s$\\\",(-1,3.5),W);\\nlabel(\\\"$r$\\\",(9,4.5),E);\\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":[]}