IMO Shortlist 2008 problem G4

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Dodao/la: arhiva
2. travnja 2012.
In an acute triangle ABC segments BE and CF are altitudes. Two circles passing through the point A anf F and tangent to the line BC at the points P and Q so that B lies between C and Q. Prove that lines PE and QF intersect on the circumcircle of triangle AEF.

Proposed by Davood Vakili, Iran
Izvor: Međunarodna matematička olimpijada, shortlist 2008