Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.

The three circles are drawn in such a way that each of them touches the other two.


So, by joining the centers of the three circles, we get,


AB = BC = CA = 2(Radius) = 7 cm


Therefore, triangle ABC is an equilateral triangle with each side 7 cm.


∴ Area of the triangle× a2


where a is the side of the triangle.




= 21.2176 cm2


Now, Central angle of each sector = = 60° (60π/180)


= π/3 radians


Thus, area of each sector = (1/2) r2θ


= (1/2) × (3.5)2 × (π/3)


=


= 6.4167 cm2


Total area of three sectors = 3 × 6.4167 = 19.25 cm2


∴ Area enclosed between three circles = Area of triangle ABC – Area of the three sectors


= 21.2176 – 19.25


= 1.9676 cm2


Hence, the required area enclosed between these circles is 1.967 cm2 (approx.).


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