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# 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

**Solution:**

Given, three circles with a radius 3.5 cm each are drawn in such a way that each of them touches the other two.

We have to find the area enclosed between these circles.

From the figure,

Three circles with centre A, B and C are drawn.

Joining the centres A, B and C forms a triangle.

AB = BC = AC = 3.5+3.5 = 7 cm

So, ABC is an equilateral triangle with sides equal to 7 cm.

Area of the equilateral triangle = (√3/4)a²

= (√3/4)(7)²

= (√3/4)(49)

= 21.218 cm²

Central angle of each sector, θ = 60°

Radius = 3.5 cm

Area of sector = πr²θ/360°

= (22/7)(3.5)²(60°/360°)

= (22/7)(3.5)²(1/6)

= 6.417 cm²

Area of 3 sectors = 3(6.417)

= 19.25 cm²

Area enclosed between three circles = area of equilateral triangle - area of 3 sectors.

= 21.218 - 19.25

= 1.968 cm²

Therefore, the area enclosed between three circles is 1.968 cm².

**✦ Try This: **Three circles each of radius 7.3 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 12

**NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 7**

## 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

**Summary:**

Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. The area enclosed between these circles is 1.968 cm²

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