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
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