Question 36
Triangle $A B C$ has a right angle at $C$, and $D$ is the foot of the altitude from $C$ to $A B$. Points $L$, $M$, and $N$ are the midpoints of segments $A D$, $D C$, and $C A$, respectively. If $C L = 7$ and $B M = 12$, compute $B N^{2}$.