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