AUSTRIAN-POLISH 2003 Problem 5
A triangle with sides a, b, c has area S.
The distances of its centroid from the vertices are x, y, z.
Show that:
if (x + y + z)^2 ≤ (a^2 + b^2 + c^2)/2 + 2S√3, then the triangle is equilateral.
Dataset text AI-MO AoPS. Quoted with source.
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