Library · Short Excursions · Geometry
Inversion in Geometry
Inversion in a circle transforms two hard problems about tangent circles into routine ones: a Pappus chain (prove that the height of the n-th circle equals 2n times its radius) and the distance between the circumscribed and inscribed circles of three mutually tangent circles of radii 1, 2, 3.
Two worked problems illustrating the power of circle inversion. The full derivations, figures, and the closing computation giving the distance between the two centres are in the PDF.