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
A Perfect Circle two became friends. Three years later, Keenan offered Howerdel, who was looking for lodging, a room in his North Hollywood home. This provided Howerdel the opportunity to play demos of his music for Keenan. Pleased with what he heard, Keenan remarked, "I can hear myself singing [those songs]." Although he originally desired a female vocalist, Howerdel agreed that Keenan would be a good fit, and A Perfect Circle was formed a short time later. The two rounded out the band's initial lineup with bassist and violinist Paz Lenchantin, former Failure guitarist Troy Van Leeuwen, and Primus drummer Tim Alexander. The