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
Catch points left the main tracks. A derail is another device used for the same purposes as catch and trap points. "Trap points" are found at the exit from a siding or where a secondary track joins a main line. A facing turnout is used to prevent any unauthorised movement that may otherwise obstruct the main line. The trap points also prevent any damage that may be done by a vehicle passing over points not set for traffic joining the main line. In the United Kingdom, the use of trap points at siding exits is required by government legislation. An unauthorised movement