Abstract
Let the points P 1, P 2, ..., P nbe given in the plane such that there are no three on a line. Then there exists a point of the plane which is contained in at least n 3/27 (open) P iPjPktriangles. This bound is the best possible.
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Boros, E., Füredi, Z. The number of triangles covering the center of an n-set. Geom Dedicata 17, 69–77 (1984). https://doi.org/10.1007/BF00181519
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DOI: https://doi.org/10.1007/BF00181519