Two circles can match any overlap exactly, so this one is always honest.
Percentages on the diagram show each region as a share of everyone (the three add up to 100%).
Each overlap is a share of the smaller of the two groups.
Percentages on the diagram show each region as a share of everyone (the seven add up to 100%).
The middle
The shaded band shows every size the middle could honestly be; the line is the size the circles are forced to draw.
Each pairwise overlap is a share of the smaller of the two groups. The triple is a share of the smallest group, capped at the tightest pairwise overlap.
Percentages on the diagram show each region as a share of everyone (the seven add up to 100%).
The shaded green stretch on each slider is the theoretical range given the other overlaps.