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.
Six Circles Theorem
See also
Circle, Contact Triangle, Hexlet, Incircle, Nine Circles Theorem, Pappus Chain, Seven Circles TheoremExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Six Circles TheoremCite this as:
Weisstein, Eric W. "Six Circles Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SixCirclesTheorem.html