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, and the radius of the circumscribed circle is
cm.

Step-by-step explanation:

From the figure, the inscribed circle is the circle inside the square. So, the radius of the inscribed circle is half the side of the square. That is 4 cm.

The circumscribed circle is the circle outside the square and its radius is half the diagonal of the square. Since the square has a side length of 8 cm, the diagonal is computed as follows, using Pythagorean Theorem using half of the square taking the diagonal as the hypotenuse.

d=\sqrt{8^2+8^2}=\sqrt{64+64}=\sqrt{128}d=

8

2

+8

2

​

=

64+64

​

=

128

​

The radius is half the diagonal. So, the radius is

\:r=\frac{\sqrt{128}}{2}=\sqrt{\frac{128}{4}}=\sqrt{32}\:r=

2

128

​

​

=

4

128

​

​

=

32

​

or (32)^(1/2).

just sum

10 + 10 = 20