Yes, that's what I meant by the solution not being trivial even for 3 points. It's either the circumscribed circle (for acute triangles) or the longest edge bei

Yes, that's what I meant by the solution not being trivial even for 3 points. It's either the circumscribed circle (for acute triangles) or the longest edge being the diameter (for obtuse triangles). For a larger number of points it's generally the same, only you don't know which of the multiple possible triangles will work.