Question

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

Answer 1

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

Now, we join centre of all three circles to each other by a line segment. Since, radius of each circle is 3.5 cm.

So; AB = 2 x Radius of circle

= 2 x 3.5 = 7 cm.

⇒ AC = BC = AB = 7cm

which shows that, ΔABC is an equilateral triangle with side 7 cm.

We know that, each angle between two adjacent sides of an equilateral triangle is 60°

∴ Area of sector with angle ∠A = 60°.

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