Circle of antisimilitude

In geometry, the circle of antisimilitude (also known as mid-circle) of two circles, α and β, is a circle for which α and β are inverses of each other. If α and β are non-intersecting or tangent, there exists one circle of antisimilitude; if α and β intersect at two points, there exist two circles of antisimilitude. When α and β are congruent, the circle of antisimilitude is degenerate; it becomes a line of symmetry, in which α and β are reflections of each other.