Question:
The maximum area of a rectangle inscribed in a circle of radius $r$ is:
The maximum area of a rectangle inscribed in a circle of radius $r$ is:
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Maximum rectangle in a circle is a square.
Updated On: Jun 10, 2026
- $\frac{3r}{4}$
- $r^2$
- $\frac{r^2}{4}$
- $2r^2$
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The Correct Option is D
Solution and Explanation
Let half sides be $x,y$:
\[
x^2 + y^2 = r^2
\]
Area:
\[
A = 4xy
\]
Maximum occurs when $x=y=\frac{r}{\sqrt{2}}$:
\[
A = 2r^2
\]
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