Circle of a sphere the Equator the only great circle. By contrast, all meridians of longitude, paired with their opposite meridian in the other hemisphere, form great circles. The diameter of the sphere which passes through the center of the circle is called its axis and the endpoints of this diameter are called its poles. A circle of a sphere can also be defined as the set of points at a given angular distance from a given pole. When the intersection of a sphere and a plane is not empty or a single point, it is a circle. This can be seen as follows:
Circle of a sphere satisfy The intersection of the spheres is the set of points satisfying both equations. Subtracting the equations gives In the singular case formula_7, the spheres are concentric. There are two possibilities: if formula_8, the spheres coincide, and the intersection is the entire sphere; if formula_9, the spheres are disjoint and the intersection is empty. When "a" is nonzero, the intersection lies in a vertical plane with this x-coordinate, which may intersect both of the spheres, be tangent to both spheres, or external to both spheres. The result follows from the previous proof for sphere-plane intersections. Circle of a sphere A