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Two circle Γ and  lies in the plane intersect at two distinct points A and B and the centre of  lies on Γ. Let points C and D be on Γ and  respectively such that C,B and D are collinear. Let points E on  be such that DE is parallel to AC. Show that AE=AB.

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If O is the entre of ∑, then we have

This shows that  ∠EAB = ∠EBA and hence AE = AB.

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