Question 182
Let $C$ be a circle with center at the origin $O$ of a system of rectangular coordinates, and let $M O N$ be the quarter circle of $C$ in the first quadrant. Let $P Q$ be an arc of $C$ of fixed length that lies in the arc $M N$. Let $K$ and $L$ be the feet of the perpendiculars from $P$ and $Q$ to $O N$, and let $V$ and $W$ be the feet of the perpendiculars from $P$ and $Q$ to $O M$, respectively. Let $A$ be the area of trapezoid $P K L Q$ and $B$ the area of trapezoid $P V W Q$. Prove that $A+B$ does not depend on where $\operatorname{arc} P Q$ is chosen.