In a circle with centre `O` and radius 5cm, AB is a chord of length `5sqrt(3)c m` . Find the area of sector `A O Bdot`

Explanation

Given: ` {AB}=5 sqrt3`


`Rightarrow AL=BL=frac{5 sqrt3}{2}`


Assume, `angle AOB=20.` So, `angle AOL=angle BOL=theta`.


In `triangle OLA`,


`sin theta=frac{AL}{OA}=frac{frac{5 sqrt{3}}{2}}{5}=frac{sqrt3}{2}`


`Rightarrow theta=60^{circ}`


`Rightarrow angle AOB=120^{circ}`


`Rightarrow ` Area of sector `AOB`


...