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

Proof:
Given: \(AB\) and \(CD\) are common tangents to two circles intersect at \(E\).
Tangents drawn through an point to a circle are equal.
\(EA = EC\) and \(EB = ED\)
Adding these two equations, we get
\(EA + \) \(= EC + \)
\(AB = CD\)
Hence proved.