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
What Is a Nation? What Is a Nation? "What is a Nation?" ("Qu'est-ce qu'une nation?") is an 1882 lecture by French historian Ernest Renan (1823–1892), known for the statements that a nation is "a daily referendum", and that nations are based as much on what the people jointly forget, as what they remember. It is frequently quoted or anthologized in works of history or political science pertaining to nationalism and national identity. Renan wrote "What is a Nation" in order to symbolize the nationalism which was born in France as a result of the French Revolution of 1789. Renan begins his essay by noting