MathDB
centroid

Source: Ireland 2005

July 6, 2009
geometryalgebrasystem of equationsgeometry proposed

Problem Statement

Let D,E D,E and F F be points on the sides BC,CA BC,CA and AB AB respectively of a triangle ABC ABC, distinct from the vertices, such that AD,BE AD,BE and CF CF meet at a point G G. Prove that if the angles AGE,CGD,BGF AGE,CGD,BGF have equal area, then G G is the centroid of △ABC \triangle ABC.
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