Question 6
A quadrilateral has one vertex on each side of a square of side-length $1$. Show that the lengths $a, b, c$ and $d$ of the sides of the quadrilateral satisfy the inequalities
$$
2 \leq a^{2}+b^{2}+c^{2}+d^{2} \leq 4
$$
$$
2 \leq a^{2}+b^{2}+c^{2}+d^{2} \leq 4
$$