Question

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___cm.
A.
(32)^(1/2)
B.
16
C.
4
D.
32
and the radius of the circumscribed circle is____cm.
A.
(32)^(1/2)
B.
2(32)^(1/2)
C.
(128)^(1/2)
D.
128

Answer 1

the radius of the inscribed circle is 16 cm.

Explanation:

The radius of the inscribed circle is equal to the length of the side of the square divided by 2. Therefore, the radius of the inscribed circle is 16 cm.

The radius of the circumscribed circle is equal to the length of the diagonal of the square divided by 2. The diagonal of a square is equal to the square root of 2 times the length of a side. Therefore, the radius of the circumscribed circle is equal to the square root of 2 times 16 cm, which is 22.63 cm.

So the answer is:

The radius of the inscribed circle is 16 cm.

The radius of the circumscribed circle is 22.63 cm.