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 line (London Underground) Circle Stock, at first painted red and cream, later painted red all over to reduce costs. These trains included first-class accommodation, but this was downgraded in 1940. From 1947 these were replaced by 5-car trains of O and P Stock, with doors remotely operated by the guard, released by the transfer of F Stock to the Uxbridge line. The 1933 London Underground Beck map shows a Metropolitan line north of and stations and a District line south of these points. On the 1947 map the Metropolitan and District lines were shown together in the same colour and two years later