Touching Circles

It is said that two circles are tangent if they have a single common point. This point is called the tangency point of the circles. Through the point of tangency, one can draw a tangent to one of the circles, which is simultaneously a tangent to another circle. Touching the circles is internal and external.
A tangency is called internal if the centers of the circles lie on one side of the tangent.
A tangency is called external if the centers of the circles lie on opposite sides of the tangent