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Prove that AB=CE

Source: Dutch IMO TST I Problem 2

July 17, 2014
trigonometrygeometrygeometric transformationreflectionprojective geometrytrig identitiesLaw of Sines

Problem Statement

Let △ABC\triangle ABC be a triangle. Let MM be the midpoint of BCBC and let DD be a point on the interior of side ABAB. The intersection of AMAM and CDCD is called EE. Suppose that ∣AD∣=∣DE∣|AD|=|DE|. Prove that ∣AB∣=∣CE∣|AB|=|CE|.
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