Isosceles right triangle A B C encloses a semicircle of area 2 \pi. The circle has its center O on hypotenuse \overline{A B} and is tangent to sides \overline{A C} and \overline{B C}. What is the area of triangle A B C ?
Answer Choices
A. 6
B. 8
C. 3 \pi
D. 10
E. 4 \pi