MEMO 2018 ekipno problem 5

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Dodao/la: arhiva
8. rujna 2018.

Let ABC be an acute-angled triangle with |AB| < |AC|, and let D be the foot of its altitude from A. Points B' and C' lie on the rays AB, AC respectively, so that points B', C' and D are collinear and points B, C, B', C' are concyclic with center O. Prove that if M is the midpoint of \overline{BC} and H is the orthocenter of ABC, then DHMO is a parallelogram.

Izvor: Srednjoeuropska matematička olimpijada 2018, ekipno natjecanje, problem 5