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In Fig. common tangents PQ and RS to two circles intersect at A. Prove that PQ = RS.

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Given: PQ and RS are the two common tangent to the two circle

To Proof: A is the point of intersection of PQ and RS

We know that , length of two tangent drawn from an exterior point to acirclr are equal.

Therefore

PA = RA----------------- (i)

QA = SA ------------------- (ii)

Adding two equations we get

PA + QA = RA + SA 

PQ =RS (proved)

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