ASU 213 All Soviet Union MO 1975 flies along triangle perimeter, centroid
Source:
July 5, 2019
geometryperimeterCentroid
Problem Statement
Three flies are crawling along the perimeter of the triangle in such a way, that the centre of their masses is a constant point. One of the flies has already passed along all the perimeter. Prove that the centre of the flies' masses coincides with the centre of masses of the triangle . (The centre of masses for the triangle is the point of medians intersection.