Power of a point P intersects the circle at A and B, the endpoints of the diameter. Their respective products of distances are equal to each other and to the power of point P in that circle This equality is sometimes known as the ""secant-tangent theorem"", ""intersecting chords theorem"", or the ""power-of-a-point theorem"". The power of a point is used in many geometrical definitions and proofs. For example, the radical axis of two given circles is the straight line consisting of points that have equal power to both circles. For each point on this line, there is a unique circle centered on that point
Area of a circle approximation among rational numbers with denominator up to 113. The number ⁄ is also an excellent approximation to , better than any other rational number with denominator less than 16604. Snell proposed (and Huygens proved) a tighter bound than Archimedes': This for "n" = 48 gives a better approximation (about 3.14159292) than Archimedes' method for "n" = 768. Let one side of an inscribed regular "n-"gon have length "s" and touch the circle at points A and B. Let A′ be the point opposite A on the circle, so that A′A is a diameter, and A′AB is an inscribed triangle