Question 49
Let $ABCD$ be a quadrilateral inscribed in a circle with center $O$. Let $P$ denote the intersection of $AC$ and $BD$. Let $M$ and $N$ denote the midpoints of $AD$ and $BC$. If $AP=1$, $BP=3$, $DP=\sqrt{3}$, and $AC$ is perpendicular to $BD$, find the area of triangle $MON$.
