Question 25
Let $ABCD$ be a quadrilateral with an inscribed circle $\omega$. Let $I$ be the center of $\omega$ and let $IA = 12$, $IB = 16$, $IC = 14$, and $ID = 11$. Let $M$ be the midpoint of segment $AC$. Compute $\frac{IM}{IN}$, where $N$ is the midpoint of segment $BD$.