Question 45
Let a quadrilateral $ABCD$ be inscribed in a circle $O$ with $\angle B$ and $\angle C$ obtuse. Let $E$ be the point of intersection of the lines $AB$ and $CD$. Let $P$ and $R$ be the feet of the perpendicular lines from $E$ to the lines $BC$ and $AD$, respectively. Let $Q$ be the point of intersection of the lines $EP$ and $AD$, and $S$ be the point of intersection of the lines $ER$ and $BC$. Let $K$ be the midpoint of the line segment $QS$. Prove that the three points $E$, $K$, $O$ are collinear.