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2001 IMO Shortlist Problems/G3

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Problem

Let ABC be a triangle with centroid G. Determine, with proof, the position of the point P in the plane of ABC such that AP{\cdot}AG + BP{\cdot}BG + CP{\cdot}CG is a minimum, and express this minimum value in terms of the side lengths of ABC.

Solution

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Resources

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Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.
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