In the given figure, common tangents AB and CD to the two circles with centers O₁ and O₂ intersect at E. Prove that AB = CD.

Question

In the given figure, common tangents AB and CD to the two circles with centers O 1 and O 2 intersect at E. Prove that AB = CD.

Philoid · Accepted Answer

Given: AB and CD are two tangents to two circles which intersects at E .

To Prove: AB = CD

Proof:

As

AE = CE …[1]

[Tangents drawn from an external point to a circle are equal]

And

EB = ED …[2]

[Tangents drawn from an external point to a circle are equal]

Adding [1] and [2]

AE + EB = CE + ED

AB = CD

Hence Proved.