Geodesic
Analogues of the Appollonian circle on the Lobachevsky plane and on sphere
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 21-32

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The analogue of the Apollonian circle on the Lobachevsky plane is a convex analytic curve. On the sphere this curve may be not convex and may be not analytic at one of its points. For the last reason, there may exist several separating sperical belts with maximal ratio of the exterior and interior radii. 
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     author = {V. A. Zalgaller and O. M. Merkulova},
     title = {Analogues of the {Appollonian} circle on the {Lobachevsky} plane and on sphere},
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V. A. Zalgaller; O. M. Merkulova. Analogues of the Appollonian circle on the Lobachevsky plane and on sphere. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 21-32. http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a2/