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

Question

Philoid · Accepted Answer

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 !