Question 101
Let $ABCD$ be a hypotenuse quadrilateral in which no 2 opposite sides are parallel. The intersection of lines $AB$ and $CD$ is denoted by $E$, and the intersection of lines $AD$ and $BC$ by $F$. The bisector of angle $\angle AFB$ intersects distance $AB$ at point $P$, and distance $CD$ at point $R$. The bisector of angle $\angle BEC$ intersects distance $BC$ at point $Q$, and distance $AD$ at point $S$. Prove that the quadrilateral $PQRS$ is a rhombus.