CircleBundleTangent

Circle Bundle of tangent circles

This is the third and last type of a [circle bundle]. The other two discussed in CircleBundles.html . It consists of all circles which are pairwise tangent at a point O (blue circles). All pairs of circles of this bundle share the same [radical axis], which is the line [OA]. Therefore some times the name (coaxal system of circles). There is no smallest/biggest circle in this bundle. With growing radius the circle tends to the common radical axis, line [OB]. Each bundle of this type defines another bundle of the same type (green circles) consisting of all circles pairwise tangent at the same point O, but having tangent there [OB], orthogonal to the previous [OA]. Every circle of the one bundle intersects orthogonally every circle of the other bundle.

Circle bundles are intimately related to [Moebius Transformations], a particular case of which are the [Inversions]. Since Moebius transformations preserve angles, they transform orthogonal bundles to orthogonal bundles. In particular, applying an appropriate inversion for each one of the three kinds of bundles one can transform them to three particular [canonical] types of bundles. This is discussed in InvertToCanonical.html .

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