MathDB
M, G, N are collinear iff MB/MA + NC/NA =1

Source: 2010 Saudi Arabia Pre-TST 1.4

December 28, 2021
geometryCentroidcollinear

Problem Statement

In triangle ABCABC with centroid GG, let M∈(AB)M \in (AB) and N∈(AC)N \in (AC) be points on two of its sides. Prove that points M,G,NM, G, N are collinear if and only if MBMA+NCNA=1\frac{MB}{MA}+\frac{NC}{NA}=1.
Back to ProblemsView on AoPS