IMO 2008 Shortlist G4

In an acute triangle ABC segments BE and CF are altitudes. Two circles passing through the points A and F are tangent to...

IMO 2008 Shortlist G4

Category: Geometry

Problem

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