OMCPLP 2020 Problem 3

Let $ABC$ be a triangle and on the sides we draw, externally, the squares $BADE, CBFG$ and $ACHI$ . Determine the greatest positive real constant $k$ such that, for any triangle $\triangle ABC$ , the following inequality is true: $[DEFGHI]\geq k\cdot [ABC]$ Note: $[X]$ denotes the area of polygon $X$ .