Question

ABCD is a square with side a. With centres A, B, C and D four circles are drawn such that each circle touches externally two of the remaining three circles. Let $\delta$ be the area of the region in the interior of the square and exterior of the circles. Then the maximum value of $\delta$ is:

• A. $a^2(1-\pi )$
• B. $a^2\left(\frac{4-\pi }{4}\right)$
• C. $a^2(\pi -1)$
• D. $\frac{\pi a^2}{4}$

Answer 1

The correct option is B

$a^2\left(\frac{4-\pi }{4}\right)$

Area of shaded region $\delta =a^2-\frac{\pi a^2}{4}$

$=a^2[1-\frac{\pi }{4}]$

$=a^2\left[\frac{4-\pi }{4}\right]$