BALTIC-WAY 1998 Problem 11

Let $a, b$ and $c$ be the lengths of the sides of a triangle with circumradius $R$. Prove that

$$R \geqslant \frac{a^{2}+b^{2}}{2 \sqrt{2 a^{2}+2 b^{2}-c^{2}}} .$$

When does equality hold?