>> should even be well-behaved on genus-0 manifolds
> 
> I take that back, it's obviously not quite well behaved on a sphere 
> (under some definitions of well-behaved) since there are no circles of 
> sufficient large radii.

Any possible line segment in elliptic geometry can be used as a circle 
diammeter. (Since lines that are "too large" to define a circle won't 
fit into the space in the first place.)

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