The picture below shows the result of applying an inversion with inversion-circle centered at B to the two bundles of CircleBundles.html . The first bundle (blue) transforms to a bundle of concentric circles, centered at A*, which is the inverse of A w.r. to the inversion circle. The second bundle (green) transforms to the bundle of lines through A*. Orthogonality is preserved as expected.
See the file InvertToCanonical2.html for the inversion of a bundle of tangent circles to a bundle of parallel lines.