Question

In the given figure common tangents AB and CD to the two circles with centres O₁ and O₂ intersect at E. Prove that AB=CD. 

Answer 1

We know that tangent segments to a circle from the same external point are congruent. 

So, we have 

EA = EC for the circle having center O₁

and 

ED = EB for the circle having center O₁ 

Now, Adding ED on both sides in EA = EC. we get

EA + ED = EC + ED

EA + EB = EC + ED

AB = CD