Q44 / 100 · BITSAT 2024 (Memory Based Paper 3) · Mathematics
The maximum area of rectangle inscribed in a circle of diameter $R$ is
- A$R^2$
- Correct answerB$\frac{R^2}{2}$
- C$\frac{R^2}{4}$
- D$\frac{R^2}{8}$
Solution
According to question,
Diameter $=R$
Diagonals, $d_1=d_2=R$
$\begin{aligned}
\text { Max Area of rectangle (any quadrilateral) } & =\frac{1}{2} d_1 \times d_2 \\
= & \frac{1}{2} \times R \times R=\frac{R^2}{2}
\end{aligned}$
Diameter $=R$
Diagonals, $d_1=d_2=R$
$\begin{aligned}
\text { Max Area of rectangle (any quadrilateral) } & =\frac{1}{2} d_1 \times d_2 \\
= & \frac{1}{2} \times R \times R=\frac{R^2}{2}
\end{aligned}$Hence, the correct answer is option: 'B'.