Question

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

Answer 1

Step-by-step explanation:

ap=ar(tangents from external point)__1

aq=as___2

add __1 and __2

ap+aq=ar+as

pq=rs

hence proved

Answer 2

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

From the property of tangents, we know that:

1. A pair of Tangents drawn from any point located exterior to the circle are Equal.

Hence, we say :

• AP = AR ...(1)
• AS = AQ ...(2)

Adding (1) and (2)

=> AP+AQ = AS+AR

=> PQ = RS

Hence we proved that PQ=RS.