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) 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