MEMO 2018 pojedinačno problem 3

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8. rujna 2018.

Let ABC be an acute-angled triangle with AB < AC and let D be the foot of its altitude from A. Let R and Q be the centroids of triangles ADB and ADC respectively. Let P be a point on the line segment \overline{BC} such that the points P, Q, R, D are concyclic.

Prove that the line AP, BQ, CR are concurrent.

Izvor: Srednjoeuropska matematička olimpijada 2016, pojedinačno natjecanje, problem 3