Question 135
Let $\triangle ABC$ be a right triangle with right angle $C$. Let $I$ be the incenter of $ABC$, and let $M$ lie on $AC$ and $N$ on $BC$, respectively, such that $M$, $I$, $N$ are collinear and $\overline{MN}$ is parallel to $AB$. If $AB = 36$ and the perimeter of $CMN$ is $48$, find the area of $ABC$.