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 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