Let \overline{A B} be a diameter of a circle and C be a point on \overline{A B} with 2 \cdot A C=B C. Let D and E be points on the circle such that \overline{D C} \perp \overline{A B} and \overline{D E} is a second diameter. What is the ratio of the area of \triangle D C E to the area of \triangle A B D ?
Answer Choices
A. \dfrac{1}{6}
B. \dfrac{1}{4}
C. \dfrac{1}{3}
D. \dfrac{1}{2}
E. \dfrac{2}{3}