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.

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.

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