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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.
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`
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