Question

The area of the square that can be inscribed in a circle of radius 8 cm is ______.

Options

• 256 cm² 

• 128 cm² 

• `64sqrt(2)` cm² 

• 64 cm² 

Answer 1

The area of the square that can be inscribed in a circle of radius 8 cm is 128 cm².

Explanation:

Given, radius of circle, r = OC = 8 cm.

∴ Diameter of the circle = AC

= 2 × OC

= 2 × 8

= 16 cm

Which is equal to the diagonal of a square.

Let side of square be x.

In right-angled ΔABC,

AC² = AB² + BC²   ...[By Pythagoras theorem]

⇒ (16)² = x² + x²

⇒ 256 = 2x²

⇒ x² = 128

∴ Area of square = x² = 128 cm²