Two circles intersect at points and , and quadrilateral is constructed so that , , , and are collinear, point on and point on are points of tangency to one of the circles, and point on and point on are points of tangency to the other circle.
If , , and , find .
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Tangents from same point are equal in length.
A S 2 = A M . A N = A P 2 So, A S = A P ( why? )
Let A S = A P = x
So, S D = 8 − x , P B = 1 2 − x
Now, S D and R D are tangents from D
So, S D = R D = 8 − x
So, C R = 1 0 − ( 8 − x ) = 2 + x ( C R = C D − R D )
Now, C R = C Q = 2 + x
Also, P B = Q B = 1 2 − x
So, B C = B Q + C Q
= 1 2 − x + 2 + x = 1 4