Mohanlal, a prosperous farmer, has a square land of side 2 km. For the current season, he decides to have some

Question

Mohanlal, a prosperous farmer, has a square land of side 2 km. For the current season, he decides to have some fun. He marks two distinct points on one of the diagonals of the land. Using these points as centers, he constructs two circles. Each of these circles falls completely within the land, and touches at least two sides of the land. To his surprise, the radii of both the circles are exactly equal to $\frac{2}{3}$ km. Mohanlal plants potatoes on the overlapping portion of these circles. Calculate the area on which Mohanlal planted potatoes (in sq. km).

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Accepted Answer

2 ( π − 2 ) 9 \frac{2(\pi - 2)}{9} 9 2 ( π − 2 ) ​. The two circles are symmetric about the diagonal. NC1= 2 2 3 \frac{2\sqrt{\ 2}}{3} 3 2 2 ​ ​ = ( 2 3 ) 2 + ( 2 3 ) 2 = ( 2 2 ) 3 \sqrt{\ \left(\frac{2}{3}\right)^{^2}+\left(\frac{2}{3}\right)^2}=\ \frac{\left(2\sqrt{\ 2}\right)}{3} ( 3 2 ​ ) 2 + ( 3 2 ​ ) 2 ​ = 3 ( 2 2 ​ ) ​ The lengths FC1, EC1 are