Power of a point P intersects the circle at A and B, the endpoints of the diameter. Their respective products of distances are equal to each other and to the power of point P in that circle This equality is sometimes known as the ""secant-tangent theorem"", ""intersecting chords theorem"", or the ""power-of-a-point theorem"". The power of a point is used in many geometrical definitions and proofs. For example, the radical axis of two given circles is the straight line consisting of points that have equal power to both circles. For each point on this line, there is a unique circle centered on that point
Circle of antisimilitude Circle of antisimilitude In inversive geometry, the circle of antisimilitude (also known as mid-circle) of two circles, "α" and "β", is a reference circle for which "α" and "β" are inverses of each other. If "α" and "β" are non-intersecting or tangent, a single circle of antisimilitude exists; if "α" and "β" intersect at two points, there are two circles of antisimilitude. When "α" and "β" are congruent, the circle of antisimilitude degenerates to a line of symmetry through which "α" and "β" are reflections of each other. If the two circles "α" and "β" cross each other, another two