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 $h(n)$.

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Let $P$ be a set of $n$ points in the plane in *general position* (no three collinear and no four concyclic), and let [ R(P)=|\\{\text{distinct radii of circumcircles of triples of }P\\}|. ] Then your $h(n)$ is exactly [ h(n)=\min_{|P|=n} R(P), ] i.e. the minimum possible number of distinct circumradii among the (\bino…

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.