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 version of the divergence theorem), in a way that avoids all mention of trigonometry and the constant . Consider the vector field formula_27 in the plane. So the divergence of r is equal to two, and hence the area of a disc "D" is equal to By Green's theorem, this is the same as the outward flux of r across the circle bounding "D": where n is the unit normal and "ds" is the arc length measure. For a circle of radius "R" centered at the origin, we have formula_30 and formula_31, so the above equality is The integral of