# The Erdös-Mordell Inequality

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.

S=PA+PB+PC

1

S=PA'+PB'+PC'

2

S≥2S

1

2