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 value of formula_72 at x. A spherical circle is the set of points a geodesic distance "R" from the zenith point z. Equivalently, with a fixed embedding into formula_73, the spherical circle of radius formula_74 centered at z is the set of x in formula_64 such that formula_76. We can also measure the area of the spherical disk enclosed within a spherical circle, using the intrinsic surface area measure on the sphere. The area of the disk of radius "R" is then given by More generally, if a sphere formula_78 has radius of curvature formula_79, then the area of the