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
Fife Circle Line the full circle to Glenrothes. Some services regularly ran through to/from until 2015, but with the opening of the Borders Railway in September that year this routing ceased (except for a small number of weekday peak trains). Here the main line and loop line divide. The two lines join forming a circle. The east peninsula of Fife beyond Kirkcaldy is not served by railways post-Beeching. At one time a railway ran all the way from Thornton to St Andrews round the coast of Fife. The Beeching Report in fact recommended services continue between Thornton and Leven but these fell victim