Question

The maximum area of a rectangle inscribed in a circle of diameter \( R \) is:

• A. \( R^2 \)
• B. \( \frac{R^2}{2} \)
• C. \( \frac{R^2}{4} \)
• D. \( \frac{R^2}{8} \)

Hint:

For a rectangle inscribed in a circle, the maximum area occurs when the diagonals are equal, and the area is half the product of the diagonals.

Answer 1

The Correct Option is B

Step 1: {Find the maximum area of the rectangle}
The diagonal of the rectangle inscribed in the circle is equal to the diameter \( R \), so the diagonal \( d = R \). The maximum area of the rectangle is given by: \[ {Max Area} = \frac{1}{2} \times d_1 \times d_2 = \frac{1}{2} \times R \times R = \frac{R^2}{2}. \]