CONO-SUR 2019 Problem 6

Let $ABC$ be an acute-angled triangle with $AB< AC$ , and let $H$ be its orthocenter. The circumference with diameter $AH$ meets the circumscribed circumference of $ABC$ at $P\neq A$ . The tangent to the circumscribed circumference of $ABC$ through $P$ intersects line $BC$ at $Q$ . Show that $QP=QH$ .