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
Curvature of a measure points "x", "y" and "z" in R, let "R"("x", "y", "z") be the radius of the Euclidean circle that joins all three of them, or +∞ if they are collinear. The Menger curvature "c"("x", "y", "z") is defined to be with the natural convention that "c"("x", "y", "z") = 0 if "x", "y" and "z" are collinear. It is also conventional to extend this definition by setting "c"("x", "y", "z") = 0 if any of the points "x", "y" and "z" coincide. The Menger-Melnikov curvature "c"("μ") of "μ" is defined to be More generally, for "α" ≥ 0, define "c"("μ")