right|thumb|200px|small circle of a sphere. right|thumb|180px|bc^2=ab^2+ac^2, where c is the center of the sphere, a is the center of the small circle, and b is a point in the boundary of the small circle. therefore, knowing the radius of the sphere, and the distance from the plane of the small circle to c, the radius of the small circle can be determined using the pythagorean theorem. a circle of a sphere is a circle that lies on a sphere. such a circle can be formed as the intersection of a sphere and a plane, or of two spheres. a circle on a sphere whose plane passes through the center of the sphere is called a great circle; otherwise it is a small circle. circles of a sphere have radius less than or equal to the sphere radius, with equality when the circle is a great circle. ==on the earth== in the geographic coordinate system on a globe, the parallels of latitude are such circles, with the equator the only great circle. by contrast, all meridians of longitude, paired with their opposite meridian in the other hemisphere, form great circles. ==related terminology== the diameter of the sphere which passes though 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. ==sphere-plane intersection== 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: let s be a sphere with center o, p a plane which intersects s. draw  perpendicular to p and meeting p at e. let a and b be any two different points in the intersection. then aoe and boe are right triangles with a common side, oe, and hypotenuses ao and bo equal. therefore the remaining sides ae and be are equal. this proves that all points in the intersection are the same distance from the point e in the plane p, in other words all points in the intersection lie on a circle c with center e.proof follows hobbs, prop. 304 this proves that the intersection of p and s is contained in c. note that oe is the axis of the circle. now consider a point d of the circle c. since c lies in p, so does d. on the other hand, the triangles aoe and doe are right triangles with a common side, oe, and legs ea and ed equal. therefore the hypotenuses ao and do are equal, and equal to the radius of s, so that d lies in s. this proves that c is contained in the intersection of p and s. as a corollary, on a sphere there is exactly one circle that can be drawn though three given points.hobbs, prop. 308 the proof can be extended to show t
Curves Rotational_symmetry Spherical_geometry