[seqfan] Intersecting circles

[Charles Greathouse]

My friend Michael asks this question: Given n (distinct) points in R^2,
what is the smallest/largest number of points on the intersections of two
circles, where for every pair (p1, p2) of points there is a circle drawn
with center p1 and radius |p1 - p2|?

This seems beautiful enough that I suspect that the sequences are already
in the OEIS, either as-is or with appropriate degeneracy conditions
(noncolinear?). Any help?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University