In \triangle A B C with side lengths A B=13, A C=12, and B C=5, let O and I denote the circumcenter and incenter, respectively. A circle with center M is tangent to the legs \overline{A C} and \overline{B C} and to the circumcircle of \triangle A B C. What is the area of \triangle M O I ?
Answer Choices
A. \dfrac{5}{2}
B. \dfrac{11}{4}
C. 3
D. \dfrac{13}{4}
E. \dfrac{7}{2}