Experimenting with the eight apollonius circles

Given three circles (blue) and their eight apollonius circles. The radiuses of the apollonius circles are connected by a formula, and this formula is used here. We see for example that the red circle is around the three blue ones, so the sign of the red circle around is positive. In the same manner the sign of the other circles are found. The sum of all the eight inverse radiuses is zero.

By moving the generating circles ( the blue ones), which can be done both by moving the centers, and by changing the size, other situations can be made. Sometimes some, or all apollonius circles disappear. But when all are there, which for example happens when the three lie outside each other, the signs can be moved to the actual situation.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com