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
Power of a point centered on the midpoint of O and P and passing through both points. It can also be shown that the point Q is the inverse of P with respect to the given circle. The "power of a point theorem", due to Jakob Steiner, states that for any line through "A" intersecting a circle "c" in points "P" and "Q", the power of the point with respect to the circle "c" is given up to a sign by the product of the lengths of the segments from "A" to "P" and "A" to "Q", with a positive sign if "A" is