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
Group of rational points on the unit circle to the origin, equal to 0. The identity in this larger group is (1,0,1,0), and the group operation is formula_9 For the group on the unit circle, the appropriate subgroup is points of form ("w","x",1,0), with formula_10 and its identity element is (1,0,1,0). The unit hyperbola group corresponds to points of form (1,0,"y","z"), with formula_11 and the identity is again (1,0,1,0). (Of course, since they are subgroups of the larger group, they both must have the same identity element.) Group of rational points on the unit circle In mathematics, the rational points on the unit circle are those points ("x",