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 of antisimilitude also orthogonal to both circles of antisimilitude. Suppose that, for three circles "α", "β", and "γ", there is a circle of antisimilitude for the pair ("α","β") that crosses a second circle of antisimilitude for the pair ("β","γ"). Then there is a third circle of antisimiltude for the third pair ("α","γ") such that the three circles of antisimilitude cross each other in two triple intersection points. Altogether, at most eight triple crossing points may be generated in this way, for there are two ways of choosing each of the first two circles and two points where the two chosen circles cross.