Question

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.

Answer 1

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`

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