Great circle. This is a circle on the surface of a sphere whose plane passes through the centre of the sphere. It will divide the sphere in to two equal hemispheres. There is only one great circle that can be drawn through any two positions unless the two positions are diametrically opposed on the sphere,in which case there is an infinite number.
Vertex of a great circle is that point on the great circle which is closest to a pole. Thus any great circle other than the equator will have two vertices,a northerly and a southerly.