Question 43
Given a triangle $ABC$ where $|BC| = a$, $|CA| = b$ and $|AB| = c$, prove that the equality
$$
\frac{1}{a+b} + \frac{1}{b+c} = \frac{3}{a+b+c}
$$
holds if and only if $\angle ABC = 60^\circ$.
$$
\frac{1}{a+b} + \frac{1}{b+c} = \frac{3}{a+b+c}
$$
holds if and only if $\angle ABC = 60^\circ$.