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 value of formula_72 at x. A spherical circle is the set of points a geodesic distance "R" from the zenith point z. Equivalently, with a fixed embedding into formula_73, the spherical circle of radius formula_74 centered at z is the set of x in formula_64 such that formula_76. We can also measure the area of the spherical disk enclosed within a spherical circle, using the intrinsic surface area measure on the sphere. The area of the disk of radius "R" is then given by More generally, if a sphere formula_78 has radius of curvature formula_79, then the area of the