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GATE 2020 EC – Question 8

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is $a$, then the area of the shaded portion is ________.

Diagram for GATE 2020 EC question 8
  1. $\pi a^2-a^2$
  2. $\pi a^2-\sqrt2a^2$
  3. $\pi a^2-2a^2$
  4. $\pi a^2-3a^2$

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Show answer and explanation

Correct answer: (C) $\pi a^2-2a^2$

Explanation

The rectangle of maximum area inscribed in a circle is a square whose diagonal is the diameter $2a$. Its side is $\sqrt2a$ and its area is $2a^2$. The shaded area is $\pi a^2-2a^2$.