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wence
@chez_jay
[Lots of edits:] I think I have it by working out the generalisation for the red area, as the area of overlap between two quarter-circles of radius r.
If they are right on top of each other, overlap area A = r * pi / 4.
If one is moved exactly r in any direction x, then they stop overlapping and A = 0.
Given that for any* 2D shape, area is directly proportional to dimension, A varies linearly but inversely with x.
[Edit 2: * this isn't right here is it, as the shape isn't just changing size]
So, generally A = - ( pi * x / 4 ) + pi / 4 [as long as r >= x >=0]
In the diagram, the distance between the two quarter-circle centres is sqrt(2).
So red area A = (pi / 4) - sqrt(2) * pi / 4
Blue area B = (pi / 4) -1.
[Edit: FFS I have misplaced something somewhere, it doesn't add up.]