A line can intersect a sphere at one point in which case it is called a tangent. It can not intersect the sphere at all or it can intersect the sphere at two points, the entry and exit points. A line that passes through the center of a sphere has two intersection points, these are called antipodal points. A plane can intersect a sphere at one point in which case it is called a tangent plane.
Lines of latitude are examples of planes that intersect the Earth sphere.
A great circle is the intersection a plane and a sphere where the plane also passes through the center of the sphere. Lines of longitude and the equator of the Earth are examples of great circles. Two points on a sphere that are not antipodal define a unique great circle, it traces the shortest path between the two points. If the points are antipodal there are an infinite number of great circles that pass through them, for example, the antipodal points of the north and south pole of Earth. Lune A lune is the area between two great circles who share antipodal points.