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Triangle ABC

Source: Indonesia Mathematics Olympiad 2006 Day 2 Problem 5

June 2, 2008
geometrygeometry proposed

Problem Statement

In triangle ABC ABC, M M is the midpoint of side BC BC and G G is the centroid of triangle ABC ABC. A line l l passes through G G, intersecting line AB AB at P P and line AC AC at Q Q, where P≠B P\ne B and Q≠C Q\ne C. If [XYZ] [XYZ] denotes the area of triangle XYZ XYZ, show that \frac{[BGM]}{[PAG]}\plus{}\frac{[CMG]}{[QGA]}\equal{}\frac32.
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