Abstract
Degenerate cases of the problem of Apollonius, to construct a circle tangent to each of three given circles, are discussed and exhaustively classified for proper circles (finite and non-zero radius). Singular cases are considered, and an outline of the extension of the problem to higher dimensions given. Amusing alternative interpretations of the results are obtained.
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References
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Pedoe, D.; “The Missing Seventh Circle”, Elemente der Mathematik, 25, 14–15. (1970).
Stoll, V.: “Zum Problem des Apollonius”, Math. Ann. 6, 613–632. (1873).
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Fitz-Gerald, J.M. A note on a problem of Apollonius. J Geom 5, 15–26 (1974). https://doi.org/10.1007/BF01954533
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DOI: https://doi.org/10.1007/BF01954533