7.62 In the figure shown, $\theta$ is measured in radians, $C$ is the center of the circle, $BCD$ and $ACE$ are straight line segments, and $AB$ is the tangent to the circle at point $A$. Given $0<\theta<\frac{\pi}{2}$, the necessary and sufficient condition for the two shaded areas to be equal is
(A) $\operatorname{tg} \theta=\theta$.
(B) $\operatorname{tg} \theta=2 \theta$.
(C) $\operatorname{tg} \theta=4 \theta$.
(D) $\operatorname{tg} 2 \theta=\theta$.
(E) $\operatorname{tg} \frac{\theta}{2}=\theta$.
(37th American High School Mathematics Examination, 1986)
［Solution］According to the problem, we have
$$
\begin{array}{l}
\therefore \quad \frac{1}{2} r^{2} \operatorname{tg} \theta-\frac{1}{2} r^{2} \theta=\frac{1}{2} r^{2} \theta \Leftrightarrow \operatorname{tg} \theta=2 \theta \text {. } \\
\end{array}
$$

Therefore, the correct choice is (B).