Question

In figure, common tangents AB and CD to two circles intersect at E. Prove that AB = CD.

Answer 1

Given: AB and CD are two tangents to two circles which intersects at E.

To Prove: AB = CD

Proof:

As

AE = CE   ......[Tangents drawn from an external point to a circle are equal] [1]

And

EB = ED   ......[Tangents drawn from an external point to a circle are equal] [2]

Adding [1] and [2]

AE + EB = CE + ED

AB = CD

Hence Proved!