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
Dividing a circle into areas Dividing a circle into areas In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with "n" sides, in such a way as to "maximise" the number of areas created by the edges and diagonals, has a solution by an inductive method. If we already have "n" points on the circle and add one more point, we draw "n" lines from the new point to previously existing points. Two cases are possible. In the first case (a), the new line passes through a point where two or more old lines (between previously existing points)