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
Circle of antisimilitude These eight or fewer triple crossing points are the centers of inversions that take all three circles "α", "β", and "γ" to become equal circles. For three circles that are mutually externally tangent, the (unique) circles of antisimilitude for each pair again cross each other at 120° angles in two triple intersection points that are the isodynamic points of the triangle formed by the three points of tangency. 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