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Let A, B, C be points on circle O such that AB is a diameter, and CO is perpendicular to AB. Let P be a point on OA, and let line CP intersect the circle again at Q. If OP = 20 and PQ = 8, find r^2, where r is the radius of the circle.

 

 Nov 4, 2020
 #1
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r^2 = 20.

 Nov 5, 2020
 #2
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QP * PC = AP * PB

 

8 * sqrt(r2 + 202) = (r - 20)*(r + 20)

 

r = 25.70069473            r2 = 660.5257097  smiley

 

jugoslav  Nov 5, 2020
edited by jugoslav  Nov 5, 2020

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