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Equivalence between sides - Portuguese MO, Problem 2, 2008

Source:

August 31, 2010
geometry proposedgeometry

Problem Statement

Let AEBCAEBC be a cyclic quadrilateral. Let DD be a point on the ray AEAE which is outside the circumscribed circumference of AEBCAEBC. Suppose that ∠CAB=∠BAE\angle CAB=\angle BAE. Prove that AB=BDAB=BD if and only if DE=ACDE=AC.
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