**How To Find The Area Of A Segment Of A Circle**

Area of the sector OPRQ = Area of the segment PRQ + Area of ∆OPQ

⇒ Area of segment PRQ =

**Read More:**

- Parts of a Circle
- Perimeter of A Circle
- Common Chord of Two Intersecting Circles
- Construction of a Circle
- The Area of A Circle
- Properties of Circles
- Sector of A Circle
- The Area of A Sector of A Circle

**Area Of A Segment Of A Circle With Examples**

**Example 1: ** Find the area of the segment of a circle,given that the angle of the sector is 120º and the radius of the circle is 21 cm. (Take π = 22/7)

**Sol. ** Here, r = 21 cm and π = 120

∴ Area of the segment

=

**Example 2: ** A chord AB of a circle of radius 10 cm makes a right angle at the centre of the circle. Find the area of major and minor segments (Take π = 3.14)

**Sol.** We know that the area of a minor segment of angle θº in a circle of radius r is given by

Here, r = 10 and θ = 90º

A = {3.14 × 25 – 50} cm^{2} = (78.5 – 50) cm^{2}

= 28.5 cm^{2}

Area of the major segment = Area of the circle – Area of the minor segment

= {3.14 × 10^{2} – 28.5} cm^{2}

= (314 – 28.5) cm^{2} = 285.5 cm^{2}

**Example 3: ** The diagram shows two arcs, A and B. Arc A is part of the circle with centre O and radius of PQ. Arc B is part of the circle with centre M and radius PM, where M is the mid-point of PQ. Show that the area enclosed by the two arcs is equal to

**Sol. ** We have,

Area enclosed by arc B and chord PQ = Area of semi-circle of radius 5 cm

Let ∠MOQ = ∠MOP = θ

In ∆OMP, we have

⇒ θ = 30º ⇒ ∠POQ = 2θ = 60º

∴ Area enclosed by arc A and chord PQ.

= Area of segment of circle of radius 10 cm and sector containing angle 60º

Hence, Required area