Dividing a circle into areas "F" can also be derived, which will solve the problem. Its vertices include the "n" points on the circle, referred to as the exterior vertices, as well as the interior vertices, the intersections of distinct chords in the interior of the circle. The "generic intersection" assumption made above guarantees that each interior vertex is the intersection of no more than two chords. Thus the main task in determining "V" is finding the number of interior vertices. As a consequence of the lemma, any two intersecting chords will uniquely determine an interior vertex. These chords are in turn uniquely determined by
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