If P is a point that is not the same as the center O of circle , the inverse of P in, or with respect to, circle  is the point Q lying on the line OP such that .

If P is a line passing through center O of circle , the inverse of P is P itself. In case P is a line not passing through center O of circle , the inverse of P is a circle Q passing though O perpendicular to P

If P is a circle passing through the center O of circle , the inverse of P is a straight line Q not passing through O and perpendicular to the diameter of  through O. In case P is a line not passing through the center O of circle , the inverse of P is a circle Q not passing through O and homothetic to circle  with O as center of homothety.

For a detailed description of Q the object created, use the routine detail (i.e., detail(Q);)

The command with(geometry,inversion) allows the use of the abbreviated form of this command.