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The area of the largest possible square inscribed in a circle of unit radius (in sq. units) is

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2 sq. units

8 sq. units

4 sq. units

5 sq. units

answer is A.

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Detailed Solution

It is given that the radius of a circle is

r = 1

.
We have to find the area of the largest possible square that can be inscribed in a circle.
The largest possible square is inscribed in a circle having circumference 2pi units. The area of the square in the square units is

The largest possible square is inscribed in a circle having circumference 2pi units. The area of the square in the square units is

The area of a circle can be expressed as

A = π r 2

, where

r

is the radius of a circle.
Then, diameter of the circle is,

r = d 2 ⇒ d = 2 r ⇒ d = 21 ⇒ d = 2

Suppose the side of the square be

a

. So, the diagonal of the square is,

d = a 2 + a 2 ⇒ d = 2 a 2 ⇒ d = 2 a

Since, the largest possible square inscribed in a circle have diagonal is equal to the diameter of circle. So,

2 a = 2 ⇒ a = 2

So, the area of the square is, Question Image

The area is 2 sq. units.
Therefore, the correct option is 1.

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