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Question
In figure, common tangents AB and CD to two circles intersect at E. Prove that AB = CD.
Solution
Given: Common tangents AB and CD to two circles intersecting at E.
To prove: AB = CD
Proof: EA = EC ...(i) [The length of tangents drawn from an internal point to a circle are equal]
And
EB = ED ...(ii) [The length of tangents drawn from an internal point to a circle are equal]
On adding equations (i) and (ii), we get
EA + EB = EC + ED
⇒ AB = CD
Hence proved.
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