<s>[INST] Length of Radius of Circle 
This problem came very straightforward to me. Since the perimeter of the square is $32,$ the sidelengths are $8.$ Since the radius of the circle is $4.$ Constructing a smaller square in the lower right hand corner with side length $4$ I can subtract the radius of the circle $4$ from the constructed diagonal of $4\sqrt2$. Then I divide by two since it's asking for the radius, and I get $2\sqrt2-2.$ Except this cannot be the answer since the integer cannot be being subtracted
 [/INST] $r=12-8 \sqrt{2}$ so $k+w+f=22$

$$GB=\frac{8\sqrt 2-8}{2}=4\sqrt 2-4\\
GH=\frac{GB}{\sqrt 2}=4- 2\sqrt 2\\
r+r\sqrt 2=4\sqrt 2-4\\
r=\frac{4\sqrt 2-4}{\sqrt 2+1}=12-8\sqrt 2$$
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