6. Four circles each of radius $x$ and a square are arranged within a circle of radius 8 as shown in the following figure.

What is the range of $x$ ?
(A) $0<x<4$;
(B) $0<x<8(\sqrt{2}+1)$;
(C) $4-2 \sqrt{2}<x<4$;
(D) $4-2 \sqrt{2}<x<8(\sqrt{2}-1)$;
(E) $4-\sqrt{2}<x<4(\sqrt{2}+1)$.
6. Answer: (D).
Consider the extreme cases:

Then $x_{\min }=\frac{8-4 \sqrt{2}}{2}=4-2 \sqrt{2}$ and $x_{\max }=\frac{8}{\sqrt{2}+1}=8(\sqrt{2}-1)$.