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
Area of a circle wrong. Suppose that the area enclosed by the circle is less than the area "T" of the triangle. Let "D" denote the deficit amount. Circumscribe a square, so that the midpoint of each edge lies on the circle. If the total area gap between the square and the circle, "G", is greater than "D", slice off the corners with circle tangents to make a circumscribed octagon, and continue slicing until the gap area is less than "D". The area of the polygon, "P", must be less than "T". This, too, forces a contradiction. For, a perpendicular to the midpoint of