IMO Shortlist 1997 problem 18

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Dodao/la: arhiva
2. travnja 2012.
The altitudes through the vertices A,B,C of an acute-angled triangle ABC meet the opposite sides at D,E, F, respectively. The line through D parallel to EF meets the lines AC and AB at Q and R, respectively. The line EF meets BC at P. Prove that the circumcircle of the triangle PQR passes through the midpoint of BC.
Izvor: Međunarodna matematička olimpijada, shortlist 1997