5) Consider a square with a unit side; inscribe a circle inside it and, within this circle, a regular hexagon. What is the length of the side of the hexagon?
(A) $1 / 2$ (B) $\sqrt{3}$
(D) $(4 \sqrt{2}-2) /$
$(\mathbf{C})$
(E) $\pi / 6$

![](https://cdn.mathpix.com/cropped/2024_04_17_241a8f7ac8d78bebac61g-1.jpg?height=220&width=235&top_left_y=121&top_left_x=2538)
5) The answer is $(\mathrm{A})$.

If the side of the square is 1, the radius of the circle inscribed in it is $1 / 2$. Remembering that the side of a hexagon inscribed in a circle has a length equal to the radius, we get the answer.