18th Turkish Mathematical Olympiad

The points $A$ and $B$ lie on a circle with diameter $CD$ and on different sides of the line $CD$. A circle $\Gamma$ passing through the points $C$ and $D$ intersects the line segment $AC$ at a point $E$ different from its endpoints, and the line $BC$ at a point $F$. $P$ is the point of intersection of the tangent line to $\Gamma$ at $E$ and the line $BC$, and $Q$ is a point different from $E$ lying on the circumcircle of the triangle $CEP$ and satisfying $QP=EP$. $S$ is the midpoint of the line segment $EQ$ and $R$ is the point of intersection of the lines $AB$ and $EF$. Show that the lines $DR$ and $PS$ are parallel.