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Locus of centroid - OIMU 1998 Problem 2

Source:

September 12, 2010
conicsellipsegeometrygeometry unsolved

Problem Statement

In a plane there is an ellipse EE with semiaxis a,ba,b. Consider all the triangles inscribed in EE such that at least one of its sides is parallel to one of the axis of EE. Find both the locus of the centroid of all such triangles and its area.
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