Good point, but is it best to give an example first or start with the axiom right away?

Also, I did use the definition of great circles (meridian). Because the term has not been explained yet.

A great circle is any circle drawn on a sphere with a radius equal to that of the sphere. So a meridian and the equator would be great circles, while the Tropic of Capricorn and the Tropic of Cancer aren't. As a result, great circles have the same centre as the sphere they are positioned on, while a circle that is not a great circles doesn't. (Using Earth as an example again, this will mean that the equator and the meridians will have the center of the inner core as their centre, while the tropics don't.)

Of course, this is assuming that the Earth is a perfect sphere, but it is a good approximation.