Inversion in a circle of a circle

Inversion in a circle, K of radius R, of a circle. The points, a, b, c, and d, are inverted in K to A, B, C, and D, respectively. If qa denotes the distance from q to a, and qA the distance from q to A, from the definition of inversion in k, qA=R*R/qa. The circle then constructed through the points A, B, and C makes clear that any circle that doesn't go through the center of K under inversion in K is a circle!