What is the non-trivial, general solution of these equal ratios? Provide non-trivial solution of the following:

$$\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}$$

$a=?, b=?, c=?$
The solution should be general.

HINT:
$\displaystyle\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}=\frac{a+b+c}{b+c+(c+a)+(a+b)}$
Similarly, 
$\displaystyle F=\frac{a}{b+c}=\frac{b}{c+a}=\frac{a-b}{b+c-(c+a)}$
Either $a=b$ or $\displaystyle F=-1$
Hope these should help
