Circles with radii of 8 and 12 cm touch internally and externally. Find the distance between the centers.

The contact of two circles internally and externally means that the smaller of the circles is inside the larger one.

The distance from the center of the larger circle to the tangent point of the smaller circle is the radius of the larger circle. At the same time, the center of the smaller circle lies on the radius of the larger circle, since this radius divides the smaller circle in half. Therefore, in order to find the distance between the centers of the circles, it is necessary to subtract the smaller one from the larger radius.

We get:

12 – 8 = 4 cm.

Answer: 4 cm.