# Triangles Are Not Always Equilateral

Algebra Level 5

What is the largest real number $$K$$ (to 2 decimal places), such that for all triangles with sides $$a, b$$ and $$c$$, the following inequality is always true:

$a^2 + b^2 + c^2 \geq K \left( a^2 + \frac{ 2abc} { a+b+c } \right).$

Note that this inequality is neither symmetric nor cyclic.

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