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A new solution of Apollonius’ problem based on stereographic projections of Möbius and Laguerre planes. (English) Zbl 1421.51001

The Apollonius problem of finding circles tangent to three given circles in the Euclidean plane, is a well-known question for which different proofs exist. The authors present a new solution based on stereographic projection using the spherical model of Möbius geometry and the cylinder model of Laguerre geometry.

MSC:

51B10 Möbius geometries
51H15 Topological nonlinear incidence structures
51B15 Laguerre geometries
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