In Fig. 10.65, common tangents PQ and RS to two circles intersect at A. Prove that PQ = RS.

Question

Philoid · Accepted Answer

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)