The North and South Poles are designations given to the points at the ends of the mathematical axis around which the Earth rotates. There is no pole through the Earth around which it turns-as seen in a globe, for example. The axis comes into being when a sphere rotates-it is a mathematical concept only. Great circles are drawn on a sphere at its greatest circumference. This is because a great circle must always have its center at the center of the sphere.
Great circles can go around a sphere at any angle.
On the Earth, a great circle perpendicular to the axis and equidistant from each pole is called the equator. None of the other lines of latitude are great circles because their planes do not go through the center of the sphere. They are parallel to the equator and smaller in circumference. We call them parallels. The longitude lines are all great circles.