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 on the unit circle in the complex plane. If "C" is the midpoint of the segment "AB", then the collection of points "P" satisfying the Apollonius condition is not a circle, but rather a line. Thus, if "A", "B", and "C" are given distinct points in the plane, then the locus of points "P" satisfying the above equation is called a "generalised circle." It may either be a true circle or a line. In this sense a line is a generalised circle of infinite radius. In every triangle a unique circle, called the incircle, can be inscribed such that it