Answer:
A great circle is any circle whose center is also the center of the sphere.
You could try this way: Spread ink on a sheet of paper. Set the sphere on the paper
so that it picks up a mark from the ink, and at the same time, place a mark on the
highest point of the sphere. Then draw any circle on the sphere that includes those
two points.
As we read the question, we were fascinated by the implication that you have
spheres with more or less than 3 dimensions.