Circles through the center invert to lines. An inversion takes circles not through the center of inversion to circles not through the center. The circumference of a circle inverts to another circle but the centers of these circles are NOT an inversive pair. Look at the following picture, Figure 4.8. Circles invert to circles.
Inversions are conformal.
A transformation is called conformal if it preserves the measure of every angle. A linkage for constructing an inversion. Show that the point Q in the linkage in Figure 4.10 always traces a straight line. Linkage for drawing a straight line. The following result demonstrates the close connection between inversion through a circle in the plane and reflections through great circles on a sphere.