Given a circle of radius *x*, a square inscribed in the circle, and another square circumscribed about the circle, what is the ratio of the perimeter of the outer square to that of the inner square?

If we draw the inner square in a foxy way, we get what we need.

As shown in the diagram, the outer perimeter is 8*x*.

The inner perimeter is 4(*x*√2) = 4*x*√2.

The ratio is | 8x |
= | 2 | = | √2 |

4x√2 |
√2 | 1 |