Two circles may touch each other either internally or externally. Let C_{1}, C_{2} be the centers of the circle and r_{1}, r_{2} be their radii and P the point of contact.

**Case 1: The two circles touch externally**

The distance between their centres is equal to the sum of their radii.

C_{1}C_{2} = r_{1} + r_{2}

**Case 2: The two circles touch internally**

The distance between their centres is equal to the difference of their radii.

C_{1}C_{2} = C_{1}P − C_{2}P = r_{1} − r_{2}