In the given figure common tangents AB and CD to the two circles with

1.	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.
Answer» 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 \(\Rightarrow\) EA + EB = EC + ED \(\Rightarrow\) AB = CD

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.

Answer»

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

\(\Rightarrow\) EA + EB = EC + ED

\(\Rightarrow\) AB = CD

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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.

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