by v_Enhance, Mar 26, 2011, 5:17 AM 
is the area of a triangle with sides 
, 
, 
, show that![\[ a^2+b^2+c^2 \geq 4\sqrt{3} T \]](http://latex.artofproblemsolving.com/6/d/7/6d7b4bce14ad4c3a71fdc54890118fef6d0a61a9.png)
by
yugrey, Mar 27, 2011, 5:42 PM
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![\[ a^2 + b^2 + c^2 \geq ab + bc + ca = 2T ( \csc \alpha + \csc \beta + \csc \gamma) \geq 2T \csc\left(\frac{\alpha + \beta + \gamma}{3}\right) = 4\sqrt{3}T \]](http://latex.artofproblemsolving.com/e/a/1/ea1948a2c5219558fedcf1627dae80e53bb56d3c.png)
