The complete question is;
Instructions:Select the correct answer from each drop-down menu.
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.
Answer:
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
