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Six Circles Theorem


Six circles theorem

Starting with a triangle, draw a circle touching two sides. Then draw a circle tangent to this circle and two other sides. Continue in the same direction. The result is a chain of circles in which the sixth circle is tangent to the first.


See also

Circle, Contact Triangle, Hexlet, Incircle, Nine Circles Theorem, Pappus Chain, Seven Circles Theorem

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References

Bogomolny, A. "Six Circles Theorem (Evelyn)." http://www.cut-the-knot.org/Curriculum/Geometry/Evelyn.shtml.Bogomolny, A. "Six Circles Theorem (Elkies)." http://www.cut-the-knot.org/Curriculum/Geometry/Elkies.shtml.Evelyn, C. J. A.; Money-Coutts, G. B.; and Tyrrell, J. A. "A Theorem about a Triangle and Six Circles." §3.3 in The Seven Circles Theorem and Other New Theorems. London: Stacey International, pp. 49-58, 1974.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 231, 1991.

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Six Circles Theorem

Cite this as:

Weisstein, Eric W. "Six Circles Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SixCirclesTheorem.html

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