The side length of the square in the figure is 8 cm. the radius of the inscribed circle is (32)^(1/2) 16 4 32 cm, and the radius of the circumscribed circle is (32)^(1/2) 2(32)^(1/2) (128)^(1/2) 128 cm.

1. the radius of the inscribed circle is   equal to 4 cm. since it is equal to the half of the length of the side of the square since the circle is tangent to one of the side of the square.
2. the radius of the circumscribed square is = to sqrt of 32 since by pythagorean theorem, the radius of the circumscribed circle is = the square of the sum of half of the side of the square ((4^2 + 4^2))^1/2   

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