Apollonius Problem from Interactive Mathematics Miscellany and Puzzles

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Apollonius Problem: What is it?
A Mathematical Droodle

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 http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

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What if applet does not run?

The applet demonstrates an ancient geometric problem of finding a circle tangent to the given three circles. The number of solutions may range from 0 to 8.

Explanation

A particular case where the three given circles touch each other externally lends itself to only two solutions that are known as Soddy's circles.

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Apollonius Problem: What is it? A Mathematical Droodle

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 http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

Apollonius Problem: What is it?
A Mathematical Droodle