Question

In Fig. 8.68, common tangents PQ and RS to two circles intersect at A. Prove that PQ=RS.

Answer 1

Given That : PQ and RS are the two common tangents to two circles

To Proof : PQ=RS

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

And, We know that, length of two tangents drawn from an exterior point to a circle are equal.

Therefore,
PA=RA-----------(i)
QA=SA---------(ii)
Adding two equations we get
PA+QA=RA+SA
PQ=RS
​Hence proved