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
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