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 by three points formula_10 not on a line is obtained by a conversion of the "3-point-form of a circle's equation" Homogeneous form<br> In homogeneous coordinates, each conic section with the equation of a circle has the form It can be proven that a conic section is a circle exactly when it contains (when extended to the complex projective plane) the points "I"(1: "i": 0) and "J"(1: −"i": 0). These points are called the circular points at infinity. In polar coordinates, the equation of a circle is: where "a" is the radius of the circle, formula_14 is the polar coordinate of