3. If $A$ is a point outside circle $\odot O$ with radius 1, $O A=2$, $A B$ is a tangent to $\odot O$ at point $B$, chord $B C \parallel O A$, and $A C$ is connected, then the area of the shaded part is
(A) $\frac{2 \pi}{9}$
(B) $\frac{\pi}{6}$
(C) $\frac{\pi}{6}+\frac{\sqrt{3}}{8}$
(D) $\frac{\pi}{4}-\frac{\sqrt{3}}{8}$
3. (B).

Connect $O B$,
$$
\begin{array}{l}
\because B C / / O A, \\
\therefore S_{\triangle O B C}=S_{\triangle A B C} .
\end{array}
$$
$\because A B$ is the tangent of the circle,
$$
\therefore O B \perp A B \text {. }
$$

In $\mathrm{Rt} \triangle A O B$, $A O=2, O B=1$,
$$
\begin{array}{l}
\therefore \angle A O B=60^{\circ} \Rightarrow \angle B O C=60^{\circ} . \\
\therefore S_{\text {crescent }}=S_{\text {sectorOBC }}=\pi \cdot \frac{1}{6}=\frac{\pi}{6} .
\end{array}
$$