## Tangent Lines

Suppose to co-planar circles $C_1$ and $C_2$ have no points in common. Determine how many lines, if any, are tangent to both $C_1$ and $C_2$?
Source: NCTM Mathematics Teacher, October 2006

Solution

When one circle is inside the other, there are no tangent lines to both circles. When the two circles are side by side, there are exactly four tangent lines to both circles.

Answer: $0$ or exactly $4$