jmc

In the configuration below, $\theta$ is measured in radians, $C$ is the center of the circle, $BCD$ and $ACE$ are line segments and $AB$ is tangent to the circle at $A$. A necessary and sufficient condition for the equality of the two shaded areas, given $0<\theta <\frac{\pi }{2}$, is $$\begin{gathered} \text{(A)}\tan \theta =\theta \text{(B)}\tan \theta =2\theta \text{(C)}\tan \theta =4\theta \text{(D)}\tan 2\theta =\theta \\ \text{(E)}\tan \frac{\theta }{2}=\theta \end{gathered}$$