Let AD be the altitude of an acute-angled triangle ABC and A′ be the point on its circumcircle opposite to A. A point P lies on the segment AD, and points X, Y lie on the segments AB, AC respectively in such a way that ∠CBP=∠ADY, ∠BCP=∠ADX. Let PA′ meet BC at point T. Prove that D, X, Y, T are concyclic. geometrySharygin Geometry OlympiadSharygin 2024