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

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

2 sq. units

8 sq. units

4 sq. units

5 sq. units

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th