Hello, Raleigh!
38. A square fits just inside a circle whole radius is $\displaystyle 3\sqrt{2}.$
There is second square that fits around that circle
and a second circle around the second square.
What is the radius of the second circle? Are they trying to be funny? . . . That first square is irrelevant!
Code:
* - - * - * - * - - * B
| * */ | _
|* R / *| 3√2
| / |
* / *
* * - - - - * A
* O 3√2 *
| |
|* *|
| * * |
* - - * - * - * - - *
The radius of the first circle is: .$\displaystyle OA = 3\sqrt{2}$
The radius of the second circle is: .$\displaystyle R \:=\:OB$
We have a 45° right triangle.
. . $\displaystyle OB^2 \:=\:OA^2 + AB^2\quad\Rightarrow\quad R^2 \:=\:(3\sqrt{2})^2 + (3\sqrt{2})^2 \:=\:18 + 18 \:=\:36$
Therefore: .$\displaystyle R \:=\:6$