IMO 2022 Shortlist G6

In an acute-angled triangle ABC, point H is the foot of the altitude from A. Let P be a moving point such that the bisec...

IMO 2022 Shortlist G6

Category: Geometry

Problem

In an acute-angled triangle ABC, point H is the foot of the altitude from A. Let P be a moving point such that the bisectors k and of angles PBC and PCB, respectively, intersect each other on the line segment AH. Let k and AC meet at E, let and AB meet at F, and let EF and AH meet at Q. Prove that, as P varies, the line PQ passes through a fixed point. (Iran)