IMO Shortlist 2017 problem G3


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Let O be the circumcenter of an acute triangle ABC. Line OA intersects the altitudes of ABC through B and C at P and Q, respectively. The altitudes meet at H. Prove that the circumcenter of triangle PQH lies on a median of triangle ABC.

Izvor: https://www.imo-official.org/problems/IMO2017SL.pdf