small circles
If you 'chop' the sphere perpendicular to the N-S axis you will get the small cicle line of latitude route. If you angle the cut downwards so it passes through the centre of the earth you will get the great circle track. In the northern hemisphere the line where the surface is sliced for the great circle will lie north of the constant latitude line. You can make any number of 'cuts' you want taking in both points by angling the blade.