**Areas related to Circles ncert solutions Chapter 12 Exercise 12.2 Question 5**

**5.** In a circle of radius 21 cm, an arc subtends an angle of at the center. Find:

(i) the length of the arc (ii) area of the sector formed by the arc

(iii) area of the segment formed by the corresponding chord

**Solution:**

is the angle subtended by arc at the center of circle and r is the radius of circle.

**Length of arc** **cm**

**Area of sector formed by arc AB=**

**Area of segment formed by arc AB= Area shaded in light blue**

**= Area of minor sector - area of triangle AOB (1)**

In ,

AO=OB {radii of circle}

{Angles opposite to equal sides are equal}

Also, we have

{Angle sum property of triangle}

Therefore, which means that is an equilateral triangle.

**Area of Equilateral Triangle =**

**(2)**

Putting equation **(2)** in **(1)**, we get

**Area of segment formed by arc AB= Area of minor sector - area of **

** **