MathDB

16

Part of 2017 BMT Spring

Problems(1)

max area of triangle of centroids of PBC, PAC,PAB 2017 BMT Individual 16

Source:

1/3/2022
Let ABCABC be a triangle with AB=3AB = 3, BC=5BC = 5, AC=7AC = 7, and let P P be a point in its interior. If GAG_A, GBG_B, GCG_C are the centroids of △PBC\vartriangle PBC, △PAC\vartriangle PAC, △PAB\vartriangle PAB, respectively, find the maximum possible area of △GAGBGC\vartriangle G_AG_BG_C.
geometrygeometric inequalityareasarea of a triangleCentroid