A generalized definition of Apollonius circles is introduced that remains unchanged in Euclidean geometry yet permits a proof that the circle of centers coincides with the equioptic curve of two circles in hyperbolic and spherical geometries.
– Szirmai, J.: Isoptic curves of conic sections in constant curvature geometries.Mathematical Communications19(2014) 277–290
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Generalized Apollonius Circles As Equioptic Curves Of Circles In Constants Curvature Geometries
A generalized definition of Apollonius circles is introduced that remains unchanged in Euclidean geometry yet permits a proof that the circle of centers coincides with the equioptic curve of two circles in hyperbolic and spherical geometries.