2018 AMC 12B Problem 21

In \triangle{ABC} with side lengths AB = 13, AC = 12, and BC = 5, let O and I denote the circumcenter and incenter, respectively. A circle with center M is tangent to the legs AC and BC and to the circumcircle of \triangle{ABC}. What is the area of \triangle{MOI}?

\textbf{(A)}\ \frac52\qquad\textbf{(B)}\ \frac{11}{4}\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ \frac{13}{4}\qquad\textbf{(E)}\ \frac72

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.