Question

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

Answer 1

Given: Common tangents AB and CD to two circles intersecting at E.

To prove: AB = CD

Proof: EA = EC   ...(i) [The length of tangents drawn from an internal point to a circle are equal]

And

EB = ED   ...(ii) [The length of tangents drawn from an internal point to a circle are equal] 

On adding equations (i) and (ii), we get

EA + EB = EC + ED

⇒ AB = CD

Hence proved.