That's partly feeding the thing that perplexes me. It's a bit like the thing about how many points you need to describe a linear alignment, in that any two points can form either a straight line or a curve. If you've got four points in any kind of square/parallelogram/trapezium, they're going to be points on some theoretical circle or other .

What if you have three of them on the perimeter then one askew then do another one for luck .