Generalization of the Apollonius Circles

Simple item page
dc.creatorPohoata, Cosmin
dc.creatorZajic, Vladimir
dc.date2008-07-07
dc.date.accessioned2026-07-07T09:48:59Z
dc.date.available2026-07-07T09:48:59Z
dc.descriptionThe three Apollonius circles of a triangle, each passing through a triangle vertex, the corresponding vertex of the cevian triangle of the incenter and the corresponding vertex of the circumcevian triangle of the symmedian point, are coaxal. Similarly defined three circles remain coaxal, when the circumcevian triangle is defined with respect to any point on the triangle circumconic through the incenter and symmedian point. Inversion in the incircle of the reference triangle carries these three coaxal circles into coaxal circles, each passing through a vertex of the inverted triangle and centered on the opposite sideline, at the intersection of the orthotransversal with respect to a point on the Euler line of the inverted triangle. A similar circumconic exists in a more general configuration, when the cevian triangle is defined with respect to an arbitrary point, passing through this arbitrary point and isogonal conjugate of its complement.
dc.description17 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0807.1131
dc.identifierhttp://arxiv.org/abs/0807.1131
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164418
dc.subjectHistory and Overview
dc.subjectMetric Geometry
dc.subject51-03; 01A20
dc.titleGeneralization of the Apollonius Circles
dc.typetext

Files

Collections

arXiv