Let ,
,
and
be three circles in the plane, and let be any circle touching and . Then build up a chain of circles such that , , , , , , where denotes a circle tangent to circles , , and . Although there are a number of choices for each successive
tangent circle in the chain, if the choice at each stage is made appropriately, then
the ninth and final circle coincides with the first circle (Evelyn et al. 1974, p. 58).
Evelyn, C. J. A.; Money-Coutts, G. B.; and Tyrrell, J. A. "The Nine Circles Theorem." §3.4 in The
Seven Circles Theorem and Other New Theorems. London: Stacey International,
pp. 58-68, 1974.Tyrrell, J. A. and Powell, M. T. "A
Theorem in Circle Geometry." Bull. London Math. Soc.3, 70-74,
1971.
,
,
and 
be three circles in the plane, and let 
be any circle touching 
and 
. Then build up a chain of circles such that 
, 
, 
, 
, 
, 
, where 
denotes a circle 
tangent to circles 
, 
, and 
. Although there are a number of choices for each successive
tangent circle in the chain, if the choice at each stage is made appropriately, then
the ninth and final circle 
coincides with the first circle 
(Evelyn et al. 1974, p. 58).
