Triangle A B C is an isosceles right triangle with A B=A C=3. Let M be the midpoint of hypotenuse \overline{B C}. Points I and E lie on sides \overline{A C} and \overline{A B}, respectively, so that A I>A E and A I M E is a cyclic quadrilateral. Given that triangle E M I has area 2, the length C I can be written as \dfrac{a-\sqrt{b}}{c}, where a, b, and c are positive integers and b is not divisible by the square of any prime. What is the value of a+b+c ?
Answer Choices
A. 9
B. 10
C. 11
D. 12
E. 13