Great circles are straight lines that go all the way around the center of the earth. The equator is a great circle. Meridians of longitude that cross over the north and south poles are also great circles. For every location on a great circle, it's antipodal location is also on the circle. Other than the equator itself, any great circle crosses the equator at two antipodal locations, 180° apart. Other than the equator and meridians of longitude that run due north and south, any great circle reaches it's maximum latitudes at two locations that are 90° of longitude east and west of the two locations where the great circle crosses the equator.
Part one
The great circle
Part two
The golden section