What geometry defines a great circle on a sphere's surface?

The intersection of the surface with a plane passing through the center.

A great circle is fundamentally defined by slicing a sphere perfectly through its exact center. The resulting edge formed where this cutting plane intersects the spherical surface constitutes the great circle. This geometric property ensures that any great circle circumference possesses the unique characteristic of dividing the sphere into two perfectly equal halves, known as hemispheres. Conversely, smaller circles on a sphere, such as lines of latitude (with the exception of the equator), do not pass through the center and thus do not meet this defining characteristic, resulting in unequal divisions of the sphere.