Sum

*AB* is a chord of a circle with centre *O* and radius 4 cm. *AB* is of length 4 cm. Find the area of the sector of the circle formed by chord *AB*.

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#### Solution

We have to find the area of the sector AOB formed by the chord AB.

We have `OA=4 cm and AB=4 cm. So,`

`AL=(AB)/2 cm`

`= 4/2 cm`

`= 2 cm`

Let ∠AOB=2θ. then,

`∠AOL=∠BOL`

=θ

In ΔOLA, We have

`sin θ=(AL)/(OA)`

`= 2/4`

`=1/2`

`θ = sin^-1 1/2`

`= 30°`

Hence, `∠AOB=60°`

Now, using the value of`∠AOB` and *r* we will find the area of sector AOB,

`A=θ/(360°) xx pir^2`

=` (60°)/(360°)xx pixx4xx4 cm^2`

`=(8pi)/3 cm^2`

`

Concept: Area of Circle

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