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arXiv · 1402.6276

Points defining triangles with distinct circumradii

Leonardo Martínez·Edgardo Roldán-Pensado
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Abstract

Paul Erdos 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 different 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.

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Leonardo Martínez, Edgardo Roldán-Pensado. 2014-02-25. Points defining triangles with distinct circumradii. https://doi.org/10.1007/s10474-014-0443-z

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