{"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":"4b293ba3-f38c-5e09-87f7-d763a29b0746","task_key":"intermediate~5falgebra--test--4b293ba3-f38c-5e09-87f7-d763a29b0746","task_revision_id":"1","upstream_id":"","short_description":"The circle $x^2 + y^2 = 2$ and the parabola $y^2 = 8x$ have two common tangents,…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"The circle $x^2 + y^2 = 2$ and the parabola $y^2 = 8x$ have two common tangents, forming four points of tangency.  Find the area of the quadrilateral formed by the four points of tangency.\\n\\n[asy]\\nunitsize(0.8 cm);\\n\\nreal upperparab (real x) {\\n  return (sqrt(8*x));\\n}\\n\\nreal lowerparab (real x) {\\n  return (-sqrt(8*x));\\n}\\n\\npair A, B, C, D;\\n\\nA = (-1,1);\\nB = (2,4);\\nC = (-1,-1);\\nD = (2,-4);\\n\\ndraw(graph(upperparab,0,3));\\ndraw(graph(lowerparab,0,3));\\ndraw(Circle((0,0),sqrt(2)));\\ndraw(interp(A,B,-0.2)--interp(A,B,1.2));\\ndraw(interp(C,D,-0.2)--interp(C,D,1.2));\\ndraw(A--C);\\ndraw(B--D);\\n\\ndot(A);\\ndot(B);\\ndot(C);\\ndot(D);\\n[/asy]\",\"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":[]}