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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.
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.