jmc

The diameter $AB$ of a circle of radius $2$ is extended to a point $D$ outside the circle so that $BD=3$. Point $E$ is chosen so that $ED=5$ and line $ED$ is perpendicular to line $AD$. Segment $AE$ intersects the circle at a point $C$ between $A$ and $E$. What is the area of $△ABC$? $\text{(A)}\frac{120}{37}\text{(B)}\frac{140}{39}\text{(C)}\frac{145}{39}\text{(D)}\frac{140}{37}\text{(E)}\frac{120}{31}$