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 $\angle ABC = 60^o$.
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Tags: geometry, angles
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 $\angle ABC = 60^o$.