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PQRS is a square ==> ABCD is a square

Source: Iran Third Round 1996, E2, P2

March 25, 2011
inequalitiesgeometrysimilar trianglesgeometry proposed

Problem Statement

Let ABCDABCD be a convex quadrilateral. Construct the points P,Q,R,P,Q,R, and SS on continue of AB,BC,CD,AB,BC,CD, and DADA, respectively, such that BP=CQ=DR=AS.BP=CQ=DR=AS. Show that if PQRSPQRS is a square, then ABCDABCD is also a square.
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