IMO Shortlist 2011 problem G4

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Dodao/la: arhiva
23. lipnja 2013.
Let ABC be an acute triangle with circumcircle \Omega. Let B_0 be the midpoint of AC and let C_0 be the midpoint of AB. Let D be the foot of the altitude from A and let G be the centroid of the triangle ABC. Let \omega be a circle through B_0 and C_0 that is tangent to the circle \Omega at a point X\not= A. Prove that the points D,G and X are collinear.

Proposed by Ismail Isaev and Mikhail Isaev, Russia
Izvor: Međunarodna matematička olimpijada, shortlist 2011