In the given figure, common tangents PQ and RS to two circles intersect at A. Prove that PQ = RS.
The figure given in the question is
We know from the property of tangents that the length of two tangents drawn from a common external point will be equal. Therefore,
PA = RA …… (1)
AQ = AS …… (2)
Let us add equation (1) and (2)
PA + AQ = RA + AS
PQ = RS
Thus we have proved that PQ = RS.