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Question:

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

Solution:

Common tangents AB and CD to the two circles with centers O1 and O2 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.