Six circles theorem

Some examples of theorem configuration changing the radius of the first circle. In the last configuration the circles are pairwise coincident.

In geometry, the six circles theorem relates to a chain of six circles together with a triangle, such that each circle is tangent to two sides of the triangle and also to the preceding circle in the chain. The chain closes, in the sense that the sixth circle is always tangent to the first circle.^[1]

The name may also refer to Miquel's six circles theorem, the result that if five circles have four triple points of intersection then the remaining four points of intersection lie on a sixth circle.

References

↑ Evelyn CJA, Money-Coutts GB, Tyrrell JA (1974). The Seven Circles Theorem and Other New Theorems. London: Stacey International. pp. 49–58. ISBN 978-0-9503304-0-2.

Wells D (1991). The Penguin Dictionary of Curious and Interesting Geometry. New York: Penguin Books. p. 231. ISBN 0-14-011813-6.

External links

Weisstein, Eric W., "Six Circles Theorem", MathWorld.
The Six Circle Theorem revisited by D. Ivanov and S. Tabachnikov