Problem 831

Erdős Problem #831: declared status 'open'. Formalized: no. Let $h(n)$ be maximal such that in any $n$ points in $\mathbb{R}^2$ (with no three on a line and no four on a circle) there are at least $h(n)$ many circles of different radii passing through three points. Estimate $h(n)$. Prize: no. Tags: geometry.