Some results of Apollonius CabriJava Illustration

Since we are involved with two disjoint circles, we assume that they are concentric.
If L, M have radii r, R respectively, then the centres of the tangent circles must lie on
the grey circles (of radii (R+r)/2, (R-r)/2). We leave this as an exercise.

In the CabriJava applet, you can vary the size of L by dragging the point B on the circumference.
You can move P or Q on their respective circles to make the tangent circles T1, T2 vary.

disjoint circles