VTMO 2026 - Grade 9 - Semifinal - SET 2 - Self-study Question 24

G is an interior point of triangle ABC. Lines AG,BG,CG meet BC,CA,AB at M,N,P respectively. Given $\dfrac{AG}{GM}+\dfrac{BG}{GN}+\dfrac{CG}{GP}=6$, prove that G is the centroid of ABC.