Problem:

A tangent line to a circle is a line that intersects the circle in exactly one point. A common tangent line to two circles is a line that is tangent to both circles. As an example, in the figure to the right, line $a$ is a common tangent to both circles, but line $b$ is only tangent to the larger circle.

Given two distinct circles in the plane, let $n$ be the number of common tangent lines that can be drawn to these two circles. What are all possible values of $n$? Your answer should include drawings with explanations.