**Question:**

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

**Solution:**

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

So, we have

EA = EC for the circle having centre O1

and

ED = EB for the circle having centre O1

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

EA + ED = EC + ED

⇒EA + EB = EC + ED

⇒AB = CD