Q10 of 34 Page 1

In the given figure, common tangents AB and CD to the two circles 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 [Tangents drawn from an external point to a circle are equal] …[1]


And


EB = ED [Tangents drawn from an external point to a circle are equal] …[2]


Adding [1] and [2]


AE + EB = CE + ED


AB = CD


Hence Proved !


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