Equilateral triange, sum... Just a short question:
In a triangle we have $\sum \left(\frac{a}{b+c}\right)^{2}$. Is the triangle equilateral?
I have derived 

$\sum\dfrac{a^2}{(b+c)^2} \geq \dfrac{(\sum \frac{a}{b+c})^2}{3} \geq \dfrac{(\frac{3}{2})^2}{3} = \dfrac{3}{4}$ by Nesbitt's inequality and Cauchy-Schwarz inequality, and equality occurs when $a = b = c$ or triangle is equilateral.
