Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The maximum area of the rectangle that can be inscribed in a circle of radius r is -
A
π r 2
B
r 2
C
D
2r 2
Text Solution
Verified by ExpertsThe correct answer is:
D
Area of rectangle
Δ = 2 
× 2x
Δ = 4x 
or Δ 2 = 16 x 2 (r 2 – x 2 )
= (16r 2 x 2 – 16x 4 ) = λ (say)
∴ 
= 32r 2 x – 16x 3 Now 
= 0, ∴ x = 
= 32r
2 – 192x 2 
= – 64r
2 < 0
Hence area maximum when x = 
∴ Maximum area = 
= 
· 
= 2r 2 .
Alternate Method : In a circle maximum are a rectangle is always square
Whose area = 
= 
= 2r 2 .
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