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If we define the radius of a circle on a sphere as being the minimum of the two possible choices (i.e. we always choose the radius that is at most π/2) then the average will be less than π/2, i.e. 7/6.
We *could* pose the question in a different way that made a great circle the average, but if we actually pick 3 random points and always choose the smaller radius, we get 7/6.