Zvonko Cerin,  The Vertex-midpoint-centroid Triangles,

Forum Geometricorum, 4 (2004) 97--109.

Abstract:  This paper explores six triangles that have a vertex, a midpoint of a side, and the centroid of the base triangle ABC as vertices. They have many interesting properties and here we study how they monitor the shape of ABC. Our results show that certain geometric properties of these six triangles are equivalent to ABC being either equilateral or isosceles.

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