Four Touching Circles III

The applet below helps verify the validity of the theorem about a chain of four circles tangent in pairs. There are four contact points. These may or may not lie in a circle. They do if the number of external tangencies at these points is even; they do not, otherwise.

All circles in the applet are draggable. Each circle is defined by its center and by a point on its border. Both points are also draggable and can be used to modify the size of the circles. To see the points check the "draggable points" checkbox.

You can invert the diagram (check "inversion") in a circle that can be dragged and resized. Letting its center overlap one of the contact points illustrates the proof of the theorem discussed on a separate page.

Try dragging the circles around as to make them touch in pairs. The applet will supply a circle if there are at least three contact points.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

What if applet does not run?

Here's one case with one pair of circles touching internally:

and another with three internal tangencies:

Relevant pages:

Inversion - Introduction

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