Question 35
Let $ABCD$ be inscribed in a circle with centre $O$. Let $E$ be the intersection point of $AC$ and $BD$. $M$ and $N$ are the midpoints of the arcs $AB$ and $CD$ respectively (the arcs not containing any other vertices). Let $P$ be the intersection point of $EO$ and $MN$. Suppose $BC = 5$, $AC = 11$, $BD = 12$ and $AD = 10$. Find $\frac{MN}{NP}$.