of radius r or a square of side length a? do you need some kind of quadruple or double integral or is there a trick? sorry, i meant two points either in the interior of said shape or on the boundary. for the circle, by symmetry, is that the same as the average distance between a point and the origin? that is, i think, 2r/3. note that the max distance is 2r and the min distance is 0.