MathNet 2010 — Part 03 Question 139

Question 139

Let $ABC$ be an equilateral triangle of center $O$ and $1$ area. Let $D$, $E$, $F$ the symmetrical points of $O$ compared to the three sides of the triangle. How much is the area in common to the $ABC$ and $DEF$ triangles?

$\frac{1}{3}$
$\frac{2 \sqrt{3}}{9}$
$\frac{\sqrt{2}}{3}$
$\frac{\sqrt{3}}{3}$
$\frac{2}{3}$.