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
Power of a point centered on the midpoint of O and P and passing through both points. It can also be shown that the point Q is the inverse of P with respect to the given circle. The "power of a point theorem", due to Jakob Steiner, states that for any line through "A" intersecting a circle "c" in points "P" and "Q", the power of the point with respect to the circle "c" is given up to a sign by the product of the lengths of the segments from "A" to "P" and "A" to "Q", with a positive sign if "A" is