SHARYGIN 2024 Problem 83

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 $\angle CBP = \angle ADY$ , $\angle BCP = \angle ADX$ . Let $PA'$ meet $BC$ at point $T$ . Prove that $D$ , $X$ , $Y$ , $T$ are concyclic.