Question

The maximum area of a rectangle inscribed in the circle $(x + 1)^2 + (y - 3)^2 = 64$ is

• A. 64 sq. units
• B. 72 sq. units
• C. 128 sq. units
• D. 8 sq. units

Answer 1

Answer: (C)

The area of a rectangle inscribed in a circle is maximum, when it is a square
The area of a rectangle inscribed in a circle is maximum, when it is a square.
$\Rightarrow (\text { diagonal })^{2}=(\text { side })^{2}+(\text { side })^{2}$
$\Rightarrow $ (diameter) $^{2}=2$ (side) $^{2}$
(because diagonal = diameter)
$\Rightarrow \frac{(16)^{2}}{2}=(\text { side })^{2}$
$\therefore $ Area $=128$ sq. units