This page gives CabriJava illustrations of the Inversion Theorem

This shows the case where we are inverting an extended line L in the Circle C.
If you move Q (on L), you will see that the image always lies on the circle L'.
This shows the case where we are invering a circle D in the circle C.
If you move P on D, you will see that P' always lies on the circle D'.

Main inversive page The Inversion Theorem