Question

In fig, 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

Common tangents $AB$ and $CD$ to the two circles with centers $O_1$ and $O_2$ intersect at $E$.

We know that Tangents drawn from an external point to a circle are equal.

So, $EA=EC$ ---- (1)

$EB=ED$ ---- (2)

Adding equation (1) and (2),

$EA+EB=EC+ED$

$AB=CD$

Hence proved.