Secant line point a "tangent line" and in no points an "exterior line". A "chord" of a circle is the line segment that joins two distinct points of the circle. A chord is therefore contained in a unique secant line and each secant line determines a unique chord. In rigorous modern treatments of plane geometry, results that seem obvious and were assumed (without statement) by Euclid in his treatment, are usually proved. For instance, "Theorem (Elementary Circular Continuity)": If formula_1 is a circle and formula_2 a line that contains a point that is inside formula_1 and a point that is outside of
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