Let $C_1$ and $C_2$ be circles of radius 1 that are in the same plane and tangent to each other. How many circles of radius 3 are in this plane and tangent to both $C_1$ and $C_2$?
$\text{(A) } 2\quad \text{(B) } 4\quad \text{(C) } 5\quad \text{(D) } 6\quad \text{(E) } 8$
There are two radius 3 circles to which $C_1$ and $C_2$ are both externally tangent.  One touches the tops of $C_1$ and $C_2$ and extends upward, and the other the other touches the bottoms and extends downward.  There are also two radius 3 circles to which $C_1$ and $C_2$ are both internally tangent, one touching the tops and encircling downward, and the other touching the bottoms and encircling upward.  There are two radius 3 circles passing through the point where $C_1$ and $C_2$ are tangent.  For one $C_1$ is internally tangent and $C_2$ is externally tangent, and for the other $C_1$ is externally tangent and $C_2$ is internally tangent.
$\fbox{D}$