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
Brocard points of the anticomplementary triangle and is also the isotomic conjugate of the symmedian point. The distance between the first two Brocard points "P" and "Q" is always less than or equal to half the radius "R" of the triangle's circumcircle: The segment between the first two Brocard points is perpendicularly bisected at the Brocard midpoint by the line connecting the triangle's circumcenter and its Lemoine point. Moreover, the circumcenter, the Lemoine point, and the first two Brocard points are concyclic—they all fall on the same circle, of which the segment connecting the circumcenter and the Lemoine point is a diameter.