SHARYGIN 2022 Problem 97

Let $H$ be the orthocenter of an acute-angled triangle $ABC$ . The circumcircle of triangle $AHC$ meets segments $AB$ and $BC$ at points $P$ and $Q$ . Lines $PQ$ and $AC$ meet at point $R$ . A point $K$ lies on the line $PH$ in such a way that $\angle KAC = 90^{\circ}$ . Prove that $KR$ is perpendicular to one of the medians of triangle $ABC$ .