When EiE_iEi occurs, all the points are packed into a 180° arc starting at point iii. The remaining arc (the gap going counterclockwise back to iii) is at least 180°. Now suppose some other point jjj also tried to be an anchor. Point jjj's clockwise semicircle is exactly 180°. But to contain all the points, it would need to bridge that gap of 180° or more while simultaneously containing point iii on the other side. A 180° arc cannot straddle a 180° gap. So EjE_jEj cannot hold.
I think we both had fun reminiscing!
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