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Question

In Figure , common tangents AB and CD to the two circles with centres $$O_1$$ and $$O_2$$ intersect at E. Prove that AB = CD.
261045_4ea7cf4255eb43dd99026fd94264c90d.png


Solution

From the given figure, $$AB$$ and $$CD$$ are common tangents on both the circles. $$AB$$ and $$CD$$ intersect at $$E$$.
Now, $$EA = EC$$ (Tangents drawn on circle from same point)
$$EB = ED$$ (Tangents drawn on circle from same point)
$$EA + EB = EC + ED$$
$$AB = CD$$

Mathematics
RS Agarwal
Standard X

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