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) , and (2) . Post a comment.
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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