Power of a point P intersects the circle at A and B, the endpoints of the diameter. Their respective products of distances are equal to each other and to the power of point P in that circle This equality is sometimes known as the ""secant-tangent theorem"", ""intersecting chords theorem"", or the ""power-of-a-point theorem"". The power of a point is used in many geometrical definitions and proofs. For example, the radical axis of two given circles is the straight line consisting of points that have equal power to both circles. For each point on this line, there is a unique circle centered on that point
Fife Circle Line the full circle to Glenrothes. Some services regularly ran through to/from until 2015, but with the opening of the Borders Railway in September that year this routing ceased (except for a small number of weekday peak trains). Here the main line and loop line divide. The two lines join forming a circle. The east peninsula of Fife beyond Kirkcaldy is not served by railways post-Beeching. At one time a railway ran all the way from Thornton to St Andrews round the coast of Fife. The Beeching Report in fact recommended services continue between Thornton and Leven but these fell victim