Geodesic
Some Theorems on Kissing Circles and Spheres
Journal for geometry and graphics, Tome 15 (2011) no. 2, pp. 159-168 Cet article a éte moissonné depuis la source Heldermann Verlag

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When three circles, O1, O2, O3, are tangent externally to each other, there are only two circles tangent to the original three circles. This is a special case of the Apollonius problem, and such circles are called the inner and outer Soddy circles. Given the outer Soddy circle S, we can construct the new Apollonian circle I1 that is tangent to S, O2, and O3. By the same method, we can construct new circles I2 tangent to S, O3, and O1, and I3 tangent to S, O1, and O2. These seven tangent circles are a subset of an Apollonian packing of circles.
Classification : 51M04, 51N10
Mots-clés : Tangent circles and spheres, inversions of circles and spheres 
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     author = {K. Morita },
     title = {Some {Theorems} on {Kissing} {Circles} and {Spheres}},
     journal = {Journal for geometry and graphics},
     pages = {159--168},
     year = {2011},
     volume = {15},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2011_15_2_JGG_2011_15_2_a3/}
}
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K. Morita . Some Theorems on Kissing Circles and Spheres. Journal for geometry and graphics, Tome 15 (2011) no. 2, pp. 159-168. http://geodesic.mathdoc.fr/item/JGG_2011_15_2_JGG_2011_15_2_a3/