Problem

Source: 2024 Turkey TST P1

Tags: geometry, incenter, circumcircle



In triangle ABC, the incenter is I and the circumcenter is O. Let AI intersects (ABC) second time at P . The line passes through I and perpendicular to AI intersects BC at X. The feet of the perpendicular from X to IO is Y. Prove that A,P,X,Y cyclic.