Please submit your concern

Question:

Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is

Explanation:

Let the two circles with centres P and Q intersect at M and N.

Quadrilateral PMQN is a square.

m ∠MPN = m ∠MQN = 90°

The area common to both the circles = 2(Area of sector P-MN – Area of ∆PMN) 

$=2\left[\left(\frac{90}{360}\times \pi \times 1^2\right)-\left(\frac{1}{2}\times 1^2\right)\right]$

$=\frac{\pi }{2}-1$

Hence, option (b).