Distinct distances from three points
Micha Sharir · 2015
Let p1, p2, p3 be three noncollinear points in the plane, and let P be a set of n other points in the plane. We show that the number of distinct distances between p1, p2, p3 and the points of P is Ω(n6/11), improving the lower bound Ω(n0.502) of Elekes and Szabo ́ [4] (and considerably simplifying the analysis).