{"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":"436a6b12-dc2e-5213-bd94-cc469c06a413","task_key":"geometry--test--436a6b12-dc2e-5213-bd94-cc469c06a413","task_revision_id":"1","upstream_id":"","short_description":"Two circles are centered at the origin, as shown. The point $P(8,6)$ is on the…","config":"geometry","split":"test","body":"{\"level\":\"Level 2\",\"problem\":\"Two circles are centered at the origin, as shown.  The point $P(8,6)$ is on the larger circle and the point $S(0,k)$ is on the smaller circle.  If $QR=3$, what is the value of $k$? [asy]\\ndefaultpen(linewidth(.7pt)+fontsize(10pt));\\ndotfactor=4;\\ndraw(Circle((0,0),7)); draw(Circle((0,0),10));\\ndot((0,0)); dot((7,0)); dot((10,0)); dot((0,7)); dot((8,6));\\ndraw((0,0)--(8,6));\\nlabel(\\\"$S (0,k)$\\\",(0,7.5),W);\\ndraw((13,0)--(0,0)--(0,13),Arrows(TeXHead));\\ndraw((-13,0)--(0,0)--(0,-13));\\n\\nlabel(\\\"$x$\\\",(13,0),E); label(\\\"$y$\\\",(0,13),N); label(\\\"$P(8,6)$\\\",(8,6),NE);\\n\\nlabel(\\\"$O$\\\",(0,0),SW); label(\\\"$Q$\\\",(7,0),SW); label(\\\"$R$\\\",(10,0),SE);\\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":[]}