KöMaL 2024 B5418

Let $a$, $b$ and $c$ denote the side lengths of acute triangle $ABC$, and let $R$ denote its circumradius. Prove that $\frac{1}{-a^2+ b^2+c^2}+\frac{1}{a^2-b^2+c^2}+\frac{1}{a^2+b^2-c^2}\ge \frac{1}{R^2},$ and find those triangles where equality holds.