2019/004) If $\frac{a}{b+ c} + \frac{b}{c+a} + \frac{c}{a+b} = 1$ then prove that $\frac{a^2}{b+ c} + \frac{b^2}{c+a} + \frac{c^2}{a+b} = 0$

We are given
$\frac{a}{b+ c} + \frac{b}{c+a} + \frac{c}{a+b} = 1$
Multiplying both sides by (a+b+c) we get
$\frac{a(a+b+c)}{b+ c} + \frac{b(a+b+c)}{c+a} + \frac{c(a+b+c)}{a+b} = a+b+c$
Or
$\frac{a^2}{b+ c} + a + \frac{b^2}{c+a} + b + \frac{c^2}{a+b} + c= a+b+c$
Or
$\frac{a^2}{b+ c} + \frac{b^2}{c+a} + \frac{c^2}{a+b} = 0$