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Another perpendicularity

Source: Benelux Mathematical Olympiad 2017, Problem 3

May 6, 2017
geometryBenelux

Problem Statement

In the convex quadrilateral ABCDABCD we have ∠B=∠C\angle B = \angle C and ∠D=90∘.\angle D = 90^{\circ}. Suppose that ∣AB∣=2∣CD∣.|AB| = 2|CD|. Prove that the angle bisector of ∠ACB\angle ACB is perpendicular to CD.CD.
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