Question

and are tangents from to the circle with centre is a point on the circle. Prove that,  

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Solution
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From the figure, there is an external point X from where two tangents, XP and XQ, are drawn to the circle. 

 

(The lengths of the tangents drawn from an external point to the circle are equal.)

Similarly,



--------- (1)

--------- (2)

By substituting in equation (1) and in equation , we get



Since the tangents and are equal, we get

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