Soddy Circles and Descartes Theorem, Three Tangent Circles. Inscribed
and Circumscribed Circles, Radii.
In the figure, circles A (radius a), B (radius b), and C (radius c) are
mutually tangent. Circle D (radius d), called inner Soddy circle, is
inscribed in circles A, B, and C. Circle E (radius e), called outer
Soddy circle, is circumscribed to circles A, B, and C. Prove that (1)
This formula is called the Descartes circle theorem since it was known to Rene Descartes (1596 - 1650). Frederic Soddy (1936) extended the result to tangent spheres.
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