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

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∠2 = 180 - ∠1

∠5 = 180 – ∠2 = 180 – (180 – ∠1)

∠5 = ∠1

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