Three circles of radius 21 cm are placed in such a way that each circle touches the other two. What is the area of the portion enclosed by the three circles?

Solution (By Examveda Team)

Area of portion enclosed by the three circles = Area of Equilateral triangle - 3 × Area of sector
$$\eqalign{ & = \frac{{\sqrt 3 }}{4} \times {\left( {{\text{side}}} \right)^2} - \left( {\pi {r^2}\left( {\frac{\theta }{{{{360}^ \circ }}}} \right) \times 3} \right) \cr & = \frac{1}{2}\left( {\frac{{\sqrt 3 }}{4} \times 42 \times 42 - \frac{{22}}{7} \times 21 \times 21 \times \frac{1}{3} \times 3} \right) \cr & = 441\sqrt 3 - 693 \cr} $$