Let $n_k$ be minimal such that if $n_k$ points in $\mathbb{R}^2$ are in general position then there exists a subset of $k$ points such that all $\binom{k}{3}$ triples determine circles of different radii.
In [Er75h] Erdős asks whether $n_k$ exists. In [Er78c] he gives a simple argument which proves that it does, and in fact
\[n_k \leq k+2\binom{k-1}{2}\binom{k-1}{3}.\]
