Abstract

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.

中文翻译：

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Steiner Inellipse的一个新性质

摘要

我们考虑了一个古老的问题，即通过给定内部点M平行于三角形的边，将三角形划分为三个相似的三角形和三个平行四边形。在此注释中，我们显示出三角形面积之和等于平行四边形面积之和的那些点M的轨迹恰好是三角形的Steiner椭圆。