The six circles theorem revisited

Dennis Ivanov, Serge Tabachnikov

Research output: Contribution to journalArticlepeer-review


The six circles theorem of C. Evelyn, G. Money-Coutts, and J. Tyrrell concerns chains of circles inscribed into a triangle: the first circle is inscribed in the first angle, the second circle is inscribed in the second angle and tangent to the first circle, the third circle is inscribed in the third angle and tangent to the second circle, and so on, cyclically. The theorem asserts that if all the circles touch the sides of the triangle, and not their extensions, then the chain is 6-periodic. We show that, in general, the chain is eventually 6-periodic but may have an arbitrarily long pre-period.

Original languageEnglish (US)
Pages (from-to)689-698
Number of pages10
JournalAmerican Mathematical Monthly
Issue number7
StatePublished - Sep 1 2016

All Science Journal Classification (ASJC) codes

  • General Mathematics


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