In figure, common tangents AB and CD to two circles intersect at E. Prove that AB = CD.
Given Common tangents AB and CD to two circles intersecting at E.
To prove AB = CD
Proof $E A=E C$ $\ldots(1)$
[the lengths of tanoents drawn from an internal point to a circle are equal]
$E B=E D$ ....(ii)
On adding Eqs. (i) and (ii), we get
$E A+E B=E C+E D$
$\Rightarrow$ $A B=C D$ Hence proved.