	It is relatively easy to show using inversion that, in the Apollonian circles, every blue circle intersects every red circle orthogonally, i.e., at a right angle. Inversion of the blue Apollonian circles with respect to a circle centered on point "C" results in a pencil of concentric circles centered at the image of point "D". The same inversion transforms the red circles into a set of straight lines that all contain the image of "D". Thus, this inversion transforms the bipolar coordinate system defined by the Apollonian circles into a polar coordinate system.