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Parallel rays in a quadrilateral

Source: Czech and Slovak Olympiad 1952, National Round, Problem 3

April 11, 2020
geometry

Problem Statement

Let ABCDABCD be a convex quadrilateral with AB=CDAB=CD. Let R,SR,S be midpoints of sides AD,BCAD,BC respectively. Consider rays AU,DVAU, DV parallel with ray RSRS and all of them point in the same direction. Show that ∠BAU=∠CDV\angle BAU=\angle CDV.
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