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On A New Property Of The Steiner Inellipse
We consider an old problem of partitioning a triangle into three similar triangles and three parallelograms by lines parallel to the sides of the triangle through a given interior point M. In this note, we show that the locus of those points M for which the sum of the triangle areas is equal to the sum of the parallelogram areas is precisely the Steiner inellipse of the triangle.
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