IMO Shortlist 1983 problem 4


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2. travnja 2012.
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On the sides of the triangle ABC, three similar isosceles triangles ABP \ (AP = PB), AQC \ (AQ = QC), and BRC \ (BR = RC) are constructed. The first two are constructed externally to the triangle ABC, but the third is placed in the same half-plane determined by the line BC as the triangle ABC. Prove that APRQ is a parallelogram.
Izvor: Međunarodna matematička olimpijada, shortlist 1983