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
Fife Circle Line line from Inverkeithing that loops back round to Kirkcaldy by an inland route via Cowdenbeath through the old Fife coalfield. Narrowly speaking, just this line could be called the Fife Circle. The current service is actually a combination of two previously separate local routes - Edinburgh to Kirkcaldy & Edinburgh to & . During the 1970s & 80s British Rail only ran a regular daytime service on the Dunfermline line as far as Cowdenbeath; & Cardenden were only served during the weekday business peaks (as can be seen from Table 242 of the UK All Line timetable of that era),