Question

In Figure , common tangents AB and CD to the two circles with centres $O_1$ and $O_2$ intersect at E. Prove that AB = CD.

Answer 1

From the given figure, $AB$ and $CD$ are common tangents on both the circles. $AB$ and $CD$ intersect at $E$.
Now, $EA=EC$ (Tangents drawn on circle from same point)

$EB=ED$ (Tangents drawn on circle from same point)

$EA+EB=EC+ED$

$AB=CD$