KöMaL 2024 B5377

Determine the set of real numbers $p$ satisfying the following property: inequality $\sqrt{a^2+b^2-ab}+\sqrt{b^2+c^2-bc}\geq \sqrt{a^2+c^2-p\cdot ac}$ holds for all triples of positive real numbers $a$, $b$ and $c$, for which the square roots are defined.