IMO Shortlist 1961 problem 2

Let $a$ , $b$ , $c$ be the sides of a triangle, and $S$ its area. Prove:
$a^{2} + b^{2} + c^{2}\geq 4S \sqrt {3}$
In what case does equality hold?

Source: Međunarodna matematička olimpijada, shortlist 1961

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