Problem

Source: 69 Polish MO 2018 Second Round - Problem 3

Tags: geometry, Plane Geometry, bisector, Poland, circumcircle



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.