  Let $S$ be a set of points in $\mathbb{R}^2$ contained in a circle and $P$ an
unrestricted point set in $\mathbb{R}^2$. We prove the number of distinct
distances between points in $S$ and points in $P$ is at least
$\min(|S||P|^{1/4-\varepsilon},|S|^{2/3}|P|^{2/3},|S|^2,|P|^2)$.
  This builds on work of Pach and De Zeeuw, Bruner and Sharir, McLaughlin and
Omar and Mathialagan on distances between pairs of sets.
