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The Erdös-Mordell Inequality

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For any triangle ABC take a point P inside ABC. Let be the sum of the distances from P to the vertices and let be the sum of the distances from P to the sides of ABC. Then , with equality holding if and only if ABC is equilateral and P is its centroid.

Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA

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