In the diagram, circles $C_{1}$ and $C_{2}$ each have center $O$. The area of the shaded region is
(A) $2 \pi$
(B) $3 \pi$
(C) $4 \pi$
(D) $6 \pi$
(E) $8 \pi$

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-112.jpg?height=577&width=534&top_left_y=205&top_left_x=1186)
Each of the two right angled triangles has hypotenuse $\sqrt{1^{2}+1^{2}}=\sqrt{2}$, so the radius of $C_{1}$ is $\sqrt{2}$ and the radius of $C_{2}$ is $2 \sqrt{2}$.

![](https://cdn.mathpix.com/cropped/2024_04_20_33a8a6559d675f59baa2g-221.jpg?height=582&width=529&top_left_y=300&top_left_x=847)

The area of the shaded region is the difference between the areas of $C_{2}$ and $C_{1}$, or

$$
\pi(2 \sqrt{2})^{2}-\pi(\sqrt{2})^{2}=8 \pi-2 \pi=6 \pi
$$

ANswer: (D)