A rectangle PQRS of maximum possible area is inscribed in a circle of radius a. Find the area of the shaded (remaining) portion of the circle.
Options:
(A) πa² − a²
(B) πa² − √2a²
(C) πa² − 2a²
(D) πa² − 3a²
Official Answer Key:
C
Step-by-Step Solution & Explanation
The maximum-area rectangle inscribed in a circle of radius a is a square with diagonal 2a, so side = 2a/√2 = a√2, area = (a√2)² = 2a². Remaining area = πa² − 2a².
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