coordinate geometry inequality geometric proof triangle square pigeonhole principle optimisation extremal principle

Problem

No solution available for this problem.

The points $A$, $B$ and $C$ lie on the sides of   a square of side 1 cm and 
no two points lie on the same side. 
Show that the length of
at least one side of the triangle $ABC$ must be less than or equal to 
$(\sqrt6 -\sqrt2)$ cm.