IMO Shortlist 2008 problem G1

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2. travnja 2012.
Let H be the orthocenter of an acute-angled triangle ABC. The circle \Gamma_{A} centered at the midpoint of BC and passing through H intersects the sideline BC at points A_{1} and A_{2}. Similarly, define the points B_{1}, B_{2}, C_{1} and C_{2}.

Prove that six points A_{1} , A_{2}, B_{1}, B_{2}, C_{1} and C_{2} are concyclic.

Author: Andrey Gavrilyuk, Russia
Izvor: Međunarodna matematička olimpijada, shortlist 2008