The radius of the inscribed circle is cm, and the radius of the circumscribed circle is cm.

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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.

Image is attached.

Radius of inscribed circle = 4 cm

Radius of circumscribed circle = 32^(1/2) cm

Step-by-step explanation:

The square has a side of 8cm.

Thus,the diameter of the inscribed circle would be same as a side of the square.

So, if diameter = 8cm, then, radius of inscribed = 8/2 = 4cm

Now, to the circumscribed circle, the diagonal of the square would be the diameter of the circumscribed circle. It can be calculated with Pythagoreas theorem.

So, d² = 8² + 8²

d² = 64 + 64

d² = 128

d = √128

Expressing it in surd form gives;

d = √32 x √4

d = 2√32 cm

So radius of circumscribed circle = (2√32)/2 = √32 cm or 32^(1/2) cm

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