Circle

There will be 3 common tangents to $C_1$ to $C_2$

There will be exactly two common tangents to $C_1$ and $C_2$

There will be no common tangent or there will be exactly two common tangents to $C_1$ and $C_2$

There will be no common tangents or there will be four common tangents to $C_1$ and $C_2$