Question

The maximum area of a rectangle that can be inscribed in a circle of radius $R$ is

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

Hint:

When optimizing geometry problems involving circles and rectangles, a square often gives the maximum area.

Answer 1

The Correct Option is C

The maximum area rectangle that can be inscribed in a circle is a square. If the diagonal of the square is equal to the diameter \(2R\), then side of square is: \[ s = \frac{2R}{\sqrt{2}} = \sqrt{2}R \] So area \(= s^2 = 2R^2\)