2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62443Let S be a set of 2n+1 points in the plane such that no three are collinear and no four are concyclic. A circle will be called point-splitting if it has 3 points of S on its circumference, n-1 points in its interior and n-1 in its exterior. We show the surprising property that S always has exactly n^2 point- splitting circles, and prove a more general result.12 pages, 4 figuresCombinatorics52C99, 05A99text