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On touching circles

Published online by Cambridge University Press:  17 October 2018

John R. Silvester
John R. Silvester*
Affiliation:
Department of Mathematics, King's College, Strand, London WC2R 2LS e-mail: jrs@kcl.ac.uk
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Extract

The circles C1, … , Cn form a chain of length n, or an n-chain, if Ci touches Ci + 1, for i = 1, … , n − 1, and the chain is closed if also Cn touches C1. If Ci touches Ci + 1 at Qi, for i = 1, … , n (subscripts being interpreted modulo n), then Q1, … , Qn (assumed distinct) are the contact points of the chain. A cyclic chain is a chain for which all the circles touch another circle S, the base circle of the chain, and if Ci touches S at Pi, then P1, … , Pn are the base points of the chain.

Type
Articles
Information
The Mathematical Gazette , Volume 102 , Issue 555 , November 2018 , pp. 460 - 470
Copyright
Copyright © Mathematical Association 2018 

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References

1. Evelyn, C. J. A., Money-Coutts, G. B. and Tyrrell, J. A., The seven circles theorem and other new theorems, Stacey International (1974).Google Scholar
2. Silvester, J. R., The seven circles theorem revisited, Math. Gaz. 102, (July 2018) pp. 280–301.Google Scholar