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.

![](https://cdn.mathpix.com/cropped/2024_04_17_6cb05c45fe7c141f3316g-1.jpg?height=184&width=252&top_left_y=732&top_left_x=1446)

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.
The possible values of $n$ are $0,1,2,3$, and 4 . These cases are illustrated below.

![](https://cdn.mathpix.com/cropped/2024_04_17_6cb05c45fe7c141f3316g-1.jpg?height=984&width=1372&top_left_y=1205&top_left_x=344)