Problem

Source: All-Russian MO 2024 9.6

Tags: geometry, circumcircle, geometry proposed



The altitudes of an acute triangle ABC with AB<AC intersect at a point H, and O is the center of the circumcircle Ω. The segment OH intersects the circumcircle of BHC at a point X, different from O and H. The circumcircle of AOX intersects the smaller arc AB of Ω at point Y. Prove that the line XY bisects the segment BC. Proposed by A. Tereshin