2006 BAMO p3 P is centroid of ABC iff P is centroid of A_1B_1C_1
Source:
August 27, 2019
Centroidmediangeometry
Problem Statement
In triangle , choose point on side , point on side , and point on side in such a way that the three segments , and intersect in one point . Prove that is the centroid of triangle if and only if is the centroid of triangle .Note: A median in a triangle is a segment connecting a vertex of the triangle with the midpoint of the opposite side. The centroid of a triangle is the intersection point of the three medians of the triangle. The centroid of a triangle is also known by the names ”center of mass” and ”medicenter” of the triangle.