The diameter \overline{A B} of a circle of radius 2 is extended to a point D outside the circle so that B D=3. Point E is chosen so that E D=5 and line E D is perpendicular to line A D. Segment \overline{A E} intersects the circle at a point C between A and E. What is the area of \triangle A B C ?

**Answer Choices**

A. \dfrac{120}{37}

B. \dfrac{140}{39}

C. \dfrac{145}{39}

D. \dfrac{140}{37}

E. \dfrac{120}{31}