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Hexagon and square

Source: Rioplatense Olympiad L3 2019

December 10, 2019
geometry

Problem Statement

Let ABCDEFABCDEF be a regular hexagon, in the sides ABAB, CDCD, DEDE and FAFA we choose four points P,Q,RP,Q,R and SS respectively, such that PQRSPQRS is a square. Prove that PQPQ and BCBC are parallel.
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