Let $A\subset {\mathbb{R}}^2$ be a set of size $n$ and let $\{d_1<\dots <d_k\}$ be the set of distinct distances determined by $A$. Let $f(d)$ be the number of times the distance $d$ is determined. Is it true that$$f(d_1)f(d_k)\le (\frac{9}{8}+o(1))n^2?$$