The intersection of a sphere with a plane that passes through the center of the sphere is called a great circle. Note that it is equivalent to say that a great circle of a sphere is any circle that lies on the surface of the sphere and has maximum circumference. Geographically speaking, longitudes are examples of great circles; however, with the exception of the equator, no latitude is a great circle.

Infinitely many great circles pass through two antipodal points of a sphere. Otherwise, two distinct points on a sphere determine a unique great circle.

An arc of a great circle is called a great arc.

Note that great circles and great arcs are geodesics of the surface of the sphere on which they lie. Thus, in spherical geometry, if a sphere is serving as the model, then lines are defined to be great circles of the sphere, and line segments are defined to be great arcs of the sphere.