IMO 2022 Shortlist G2
In the acute-angled triangle ABC, the point F is the foot of the altitude from A, and P is a point on the segment AF. Th...
Category: Geometry
Problem
In the acute-angled triangle ABC, the point F is the foot of the altitude from A, and P is a point on the segment AF. The lines through P parallel to AC and AB meet BC at D and E, respectively. Points X ‰ A and Y ‰ A lie on the circles ABD and ACE, respectively, such that DA “ DX and EA “ EY . Prove that B, C, X and Y are concyclic. (Netherlands)