In fig common tangents PQ and RS to two circles intersect at A. Prove that PQ = RS.
Two circles namely (i) & (ii) as shown with common tangents as PQ and RS.
We know that
The tangents from external point to the circle are equal in length.
From A to circle (i) AP = AR … (i)
From A to circle (ii), AQ = AS …. (ii)
(i) + (ii) ⇒ AP + AQ = AR + RS
⇒ PQ = RS
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