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 wrong. Suppose that the area enclosed by the circle is less than the area "T" of the triangle. Let "D" denote the deficit amount. Circumscribe a square, so that the midpoint of each edge lies on the circle. If the total area gap between the square and the circle, "G", is greater than "D", slice off the corners with circle tangents to make a circumscribed octagon, and continue slicing until the gap area is less than "D". The area of the polygon, "P", must be less than "T". This, too, forces a contradiction. For, a perpendicular to the midpoint of