HMMT 2011 U21

Let $A B C D$ be a quadrilateral inscribed in a circle with center $O$. Let $P$ denote the intersection of $A C$ and $B D$. Let $M$ and $N$ denote the midpoints of $A D$ and $B C$. If $A P=1, B P=3, D P=\sqrt{3}$, and $A C$ is perpendicular to $B D$, find the area of triangle $M O N$.