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Question

In a circle of radius 'r' and center 'O', P and Q are points on the circle such that OP OQ.

Suppose PQ = a = 12. Find PQ in terms of a and r.


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Solution

Refer to the following figure. Since P and Q are points on the circle, 

OP = OQ = r. Since OPQ is a right angled triangle, 

PQ2 = QP2 + OQ2 = 2r2

 PQ = r2

Since a = 12,

2a = 2

So, PQ = r(2a) = 2ar

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