Secant line point a "tangent line" and in no points an "exterior line". A "chord" of a circle is the line segment that joins two distinct points of the circle. A chord is therefore contained in a unique secant line and each secant line determines a unique chord. In rigorous modern treatments of plane geometry, results that seem obvious and were assumed (without statement) by Euclid in his treatment, are usually proved. For instance, "Theorem (Elementary Circular Continuity)": If formula_1 is a circle and formula_2 a line that contains a point that is inside formula_1 and a point that is outside of
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