In the given figure common tangents AB and CD to the two circles with centres O_{1} and O_{2} intersect at E. Prove that AB=CD

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#### 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 O_{1}

and

ED = EB for the circle having center O_{1 }

Now, Adding ED on both sides in EA = EC. we get

EA+ ED = EC + ED

⇒ EA + EB = EC + ED

⇒ AB = CD

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

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