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Singapore Mathematical Olympiad 2009 Problem 1

Source:

August 3, 2010
geometryCentroidTriangleIMO ShortlistIMO Longlist

Problem Statement

Given triangle ABC ABC with points M M and N N are in the sides AB AB and AC AC respectively. If BMMA+CNNA=1 \dfrac{BM}{MA} +\dfrac{CN}{NA} = 1 , then prove that the centroid of ABC ABC lies on MN MN .
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