Question

If 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 intersect at E
To prove: AB =CD
Proof:
EA = EC ...(i)
[The lengths of tangents drawn from an internal point to a circle are equal]
EB = ED ...(ii)
On adding eqs. (i) and (ii) , we get
EA + EB = EC + ED
$\Rightarrow$ AB = CD Hence proved.