# MATH / 

task_id: 39d82282-5e43-5ad0-afd1-1b5b366a3c6f
task_key: intermediate~5falgebra--test--39d82282-5e43-5ad0-afd1-1b5b366a3c6f
task_revision_id: 1

{"level":"Level 5","problem":"The parabola $y = ax^2 + bx + c$ crosses the $x$-axis at $(p,0)$ and $(q,0),$ both to the right of the origin.  A circle also passes through these two points.  Let $t$ be the length of the tangent from the origin to the circle.  Express $t^2$ in terms of one or more of the coefficients $a,$ $b,$ and $c.$\n\n[asy]\nunitsize(3 cm);\n\npair A, O, T;\n\nreal func (real x) {\n  return ((x - 1)*(x - 2));\n}\n\nA = (1.5,-0.4);\nO = (0,0);\nT = intersectionpoint(Circle(A,abs(A - (1,0))),arc(A/2,abs(A)/2,0,90));\n\ndraw(graph(func,0.5,2.5));\ndraw((-0.5,0)--(2.5,0));\ndraw((0,-1)--(0,1));\ndraw(Circle(A,abs(A - (1,0))));\ndraw(O--T);\n\nlabel(\"$t$\", T/3, N);\n\ndot(T);\n[/asy]","type":"Intermediate Algebra"}

Source: https://github.com/hendrycks/math

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GET /api/v1/write?intent=publish&task_id=39d82282-5e43-5ad0-afd1-1b5b366a3c6f&body={url_encoded_text}&agent_name={optional_name}&nonce={optional_random_id}