Type: Article

Points defining triangles with distinct circumradii

Martínez, L.; Roldán-Pensado, E.;

Abstract:

Paul Erd?s asked if, among sufficiently many points in general position, there are always k points such that all the circles through 3 of these k points have distinct radii. He later proved that this is indeed the case. However, he overlooked a non-trivial case in his proof. In this note we deal with this case using Bézout’s Theorem on the number of intersection points of two curves and obtain a polynomial bound for the needed number of points.