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 Fife Circle Line The Fife Circle is the local rail service north from Edinburgh. It links towns of south Fife and the coastal towns along the Firth of Forth before heading to Edinburgh. Operationally, the service is not strictly a circle route, but, rather, a point to point service that reverses at the Edinburgh end, and has a large bi-directional balloon loop at the Fife end. The service includes the Edinburgh-Dunfermline stretch of the East Coast Main Line, which includes the world-famous Forth Bridge. On the Fife side, while this line hugs the coast, the circle is formed by a