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Existence of square with properties

Source: China Mathematical Olympiad 2016 Q5

December 17, 2015
geometry

Problem Statement

Let ABCDABCD be a convex quadrilateral. Show that there exists a square A′B′C′D′A'B'C'D' (Vertices maybe ordered clockwise or counter-clockwise) such that A≠A′,B≠B′,C≠C′,D≠D′A \not = A', B \not = B', C \not = C', D \not = D' and AA′,BB′,CC′,DD′AA',BB',CC',DD' are all concurrent.
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