Question 172
Find all positive real numbers $a, b, c$, which satisfy the equality:
$$
ab\left(1 - \frac{c^2}{(a+b)^2}\right) = bc\left(1 - \frac{a^2}{(b+c)^2}\right) = ca\left(1 - \frac{b^2}{(c+a)^2}\right).
$$
$$
ab\left(1 - \frac{c^2}{(a+b)^2}\right) = bc\left(1 - \frac{a^2}{(b+c)^2}\right) = ca\left(1 - \frac{b^2}{(c+a)^2}\right).
$$