(A) Hull is _not_ a quadrilateral if the 4th point lies inside the
triangle AND _many_ other points. For instance, extend the
perpendicular bisector (just as a sample case) of any one side beyond
the vertex of the triangle that it passes through.

The same triangle reasoning holds good here too right? If we choose the end
points of the side that we are bisecting and the new point we are choosing
on the perpendicular bisector as the triangle the other vertex will be
inside the triange?

I dont think i am getting the example correctly...

(B) If we consider the plane as a unit square, then limiting
assertions on the probability (like the one you made about three
points being collinear) become less accurate

Well this is not a real issue because even then the definition of a point is
such that there are infinite points in a unit square so the assertion
remains accurate

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