source ...The shortest path between two points on a sphere, also known as an orthodrome, is a segment of a great circle.
Great Circle -- from Wolfram MathWorld
Is it true the for any 2 points on the surface of a sphere it is possible to draw a great circle that passes through both points?
I have a few follow up questions about this but will wait for a response before I launch into unfounded conjecture
Thanks my follow up question is this, if using the same 2 points I construct a another circle on the sphere's surface (not a great circle this time) how would I prove that the segment of this new circle is greater then the great circle segment between the same points?
I think it must have something to do with the curvature of the circles but am having trouble visualising it?