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
Area of a circle approximation among rational numbers with denominator up to 113. The number ⁄ is also an excellent approximation to , better than any other rational number with denominator less than 16604. Snell proposed (and Huygens proved) a tighter bound than Archimedes': This for "n" = 48 gives a better approximation (about 3.14159292) than Archimedes' method for "n" = 768. Let one side of an inscribed regular "n-"gon have length "s" and touch the circle at points A and B. Let A′ be the point opposite A on the circle, so that A′A is a diameter, and A′AB is an inscribed triangle