PL-OM 2018 Problem 3

Bisector of side $BC$ intersects circumcircle of triangle $ABC$ in points $P$ and $Q$ . Points $A$ and $P$ lie on the same side of line $BC$ . Point $R$ is an orthogonal projection of point $P$ on line $AC$ . Point $S$ is middle of line segment $AQ$ . Show that points $A, B, R, S$ lie on one circle.