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
Concyclic points of a regular polygon of any number of sides are concyclic. A tangential polygon is one having an inscribed circle tangent to each side of the polygon; these tangency points are thus concyclic on the inscribed circle. A convex quadrilateral is orthodiagonal (has perpendicular diagonals) if and only if the midpoints of the sides and the feet of the four altitudes are eight concyclic points, on what is called the eight-point circle. Concyclic points In geometry, a set of points are said to be concyclic (or cocyclic) if they lie on a common circle. All concyclic points are the same