Three circles of equal radius ‘a’ cm touch each other.

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Three circles of equal radius ‘a’ cm touch each other. The area of the shaded region is :

Using Rule 6 and 17,

Let AB = BC = CA = 2a cm.
∠BAC = ∠ACB = ∠ABC = 60°

Area of ∆ABC =	√3	× (side)²
	4

=	√3	× 4a²
	4

= √3a² sq.cm.

Area of three sectors = 3 ×	60	× π × a²
	360

=	πa²	× sq.cm.
	2

Area of the shaded region = √3a² -	π	× sq.cm.
	2

=		2√3 - π		a² sq.cm.
		2