In search of more triangle centres. A source of classroom projects in Euclidean geometry

Two more triangle centers

“…Proof. It is obvious that the medians A A , B B , CC of ABC divide ABC into six triangles of equal areas; see [1,Theorem 5]. Therefore the quadrilaterals GC AB , G A BC , G B C A have equal areas.…”

Equality of areas among the ears of the Routh triangle

“…Such questions have appeared in the literature. For example, it is proved in [5,Theorem 5] that if the areas of the six subtriangles in Figure 4 are denoted by À to Å, then the following conditions are equivalent:…”