If we are given that:

$\displaystyle \frac{b + c - a}{1} = \frac{a + c - b}{2} = \frac{a + b - c}{3}$, how to find $\displaystyle a : b : c$?

(I was solving a trigonometry in triangles question, and I needed to find out $\displaystyle a:b:c$. I found that $\displaystyle \frac{s - a}{1} = \frac{s - b}{2} = \frac{s - c}{3}$, where s is semi-perimeter. Hence, the the given equation. On second thought, is there any way to find $\displaystyle a:b$ if we know $\displaystyle \frac{k + a}{k + b} = \lambda$, where k and $\displaystyle \lambda$ are known constants?)