Circle $1$ is circumscribed about a square of side $8$ and circle $2$ is inscribed in the square Circle $1$ is circumscribed about a square of side $8$ and circle $2$
  is inscribed in the square. What is the ratio of the area of circle
  $1$ to circle $2$?


I know the formula of a circle is $A=\pi r^2$ but does anyone know how I can find the radius of circle $1$ and circle $2$?
The circle inscribed in the square has a radious $r_1=4$, because it touches the sides of the square at the middle points. While the circle ciscunscribed about the square has a radious of $r_2=4\sqrt{2}$ becouse it touches the vertex of the square (its radious is just half of the diagonal of the square). Finally, the ratio between the areas of both circles is just the difference
\begin{equation}
A_2/A_1=\frac{\pi r_{2}^2}{\pi r_{1}^2}=2
\end{equation}
Their radius are $4$ and $1$ respectively.
So the ratio should be 
$$\frac{4^2}{1^2} = 16$$