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
Circle line (London Underground) the southern portion of the line. Due to conflict between the two companies it was not until October 1884 that the inner circle was completed. The line was electrified in 1905, and in 1933 the companies were amalgamated into the London Passenger Transport Board. In 1949 the Circle line appeared as a separate line for the first time on the Tube map. In 2009 the closed loop around the centre of London on the north side of the River Thames was broken at Edgware Road and extended west to become a spiral to Hammersmith. The signalling system is being upgraded