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Question
In the given figure common tangents AB and CD to the two circles with centres O1 and O2 intersect at E. Prove that AB=CD
Solution
We know that tangent segments to a circle from the same external point are congruent.
So, we have
EA = EC for the circle having center O1
and
ED = EB for the circle having center O1
Now, Adding ED on both sides in EA = EC. we get
EA+ ED = EC + ED
⇒ EA + EB = EC + ED
⇒ AB = CD
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