jmc

In the adjoining figure, $AB$ is a diameter of the circle, $CD$ is a chord parallel to $AB$, and $AC$ intersects $BD$ at $E$, with $\angle AED=\alpha$. The ratio of the area of $△CDE$ to that of $△ABE$ is $\text{(A)}\cos \alpha \text{(B)}\sin \alpha \text{(C)}{\cos }^2\alpha \text{(D)}{\sin }^2\alpha \text{(E)}1-\sin \alpha$