An area formula for the triangle of residual centroids and its generalizations


 András, Szilárd and Kiss, Sándor Nagydobai


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In this paper we consider an inscribed triangle XYZ to a triangle ABC and we establish a relation between the area of these two triangles and the area of the triangle determined by the centroids of the residual triangles AZY, BXZ and CYX. Moreover we generalize this relation to the case of a general barycenter instead of centroid and also to quadrilaterals.

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 András, Szilárd ,  Kiss, Sándor Nagydobai