Given: Common tangents AB and CD to two circles intersect at E
To prove: AB =CD
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/15538/content_1.png)
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
⇒ AB = CD Hence proved.