In figure, common tangents \(AB\) and \(CD\) to two circles intersect at \(E\). Prove that \(AB = CD\).
 
YCIND_240308_6083_circles_36.png
 
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.