Question

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.

Answer 1

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

The radius is half the diagonal. So, the radius is
     $\:r=\frac{\sqrt{128}}{2}=\sqrt{\frac{128}{4}}=\sqrt{32}\:$  or (32)^(1/2).

Answer 2

The radius of the inscribed circle and circumscribed circles are 4cm and √32 respectively.

It is given that,

The side length of the square PQRS = 8cm

What is a circle?

A circle is the locus of a point in a plane such that the distance of this point from a fixed point is always the same.

We can say that side of the square will be the diameter of the inscribed circle.

So diameter of inscribed circle = 8cm

Radius of inscribed circle = 4cm

We can say that the diagonal of the square will be the diameter of the circumscribed circle.

Diagonal of square= √(8)^2 + (8)^2 =8√2.

Diameter of circumscribed circle = 8√2.

Radius of circumscribed circle = 4√2 = √32.

Therefore, the radius of the inscribed circle and circumscribed circles are 4cm and √32 respectively.

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