A circle with center $A$ and radius three inches is tangent at $C$ to a circle with center $B$, as shown. If point $B$ is on the small circle, what is the area of the shaded region? Express your answer in terms of $\pi$.
The radius of the bigger circle is the diameter of the smaller circle. The area of the bigger circle is (2*3)^2*pi or 36pi. The small circle is 3^2*pi or 9pi. The area of the shaded region is 36pi - 9pi=27pi