2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58607The orthocentroidal circle of a nonequilateral triangle has diameter GH, joining the centroid to the orthocenter. We show that the incenters of triangles with a given Euler line simply cover the interior of the orthocentroidal circle, and that their Fermat points also lie within this circle.7 pages, Latex2e, 4 figuresMetric Geometry51M04text