IMO Shortlist 2009 problem G2

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Dodao/la: arhiva
2. travnja 2012.
Let ABC be a triangle with circumcentre O. The points P and Q are interior points of the sides CA and AB respectively. Let K,L and M be the midpoints of the segments BP,CQ and PQ. respectively, and let \Gamma be the circle passing through K,L and M. Suppose that the line PQ is tangent to the circle \Gamma. Prove that OP = OQ.

Proposed by Sergei Berlov, Russia
Izvor: Međunarodna matematička olimpijada, shortlist 2009