Number of Common Tangents

Number of Common Tangents

For two circles with centre distance $$d$$:

$$d>r_1+r_2\Rightarrow4\text{ common tangents}$$

$$d=r_1+r_2\Rightarrow3\text{ common tangents}$$

$$|r_1-r_2|<d<r_1+r_2\Rightarrow2\text{ common tangents}$$

$$d=|r_1-r_2|\Rightarrow1\text{ common tangent}$$

$$d<|r_1-r_2|\Rightarrow0\text{ common tangents}$$

Usage

- Used to determine the number of common tangents between two circles.