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The Erdös-Mordell Inequality

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.

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"The Erdös-Mordell Inequality" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/TheErdoesMordellInequality/
Contributed by: Jay Warendorff
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US Common Core State Standards, Mathematics