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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) Inner Soddy Circle Formula, and (2) Outer Soddy Circle Formula. Post a comment.


Soddy, Descartes, Circles, Theorem 

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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