In a circle of centre o and r =5cm Ab is a third of length 5√3cm . Find the area of the sector AOB

In a circle of centre o and r =5cm Ab is a third of length 5√3cm . F

1.	In a circle of centre o and r =5cm Ab is a third of length 5√3cm . Find the area of the sector AOB
Answer» It is given that AB = 5{tex}\\sqrt3{/tex}\xa0cm.{tex}\\Rightarrow \\quad A L = B L = \\frac { 5 \\sqrt { 3 } } { 2 } \\mathrm { cm }{/tex}Let\xa0{tex}\\angle {AOB}=2\\theta{/tex} . Then,\xa0{tex}\\angle A O L = \\angle B O L = \\theta{/tex}In\xa0{tex}\\triangle{/tex}OLA, we have{tex}\\sin \\theta = \\frac { A L } { O A } = \\frac { \\frac { 5 \\sqrt { 3 } } { 2 } } { 5 } = \\frac { \\sqrt { 3 } } { 2 }{/tex}{tex}\\Rightarrow \\quad \\theta = 60 ^ { \\circ }{/tex}{tex}\\Rightarrow \\quad \\angle A O B = 120 ^ { \\circ }{/tex}{tex}\\therefore{/tex}Area of sector AOB =\xa0{tex}\\frac { 120 } { 360 } \\times \\pi \\times 5 ^ { 2 } \\mathrm { cm } ^ { 2 } = \\frac { 25 \\pi } { 3 } \\mathrm { cm } ^ { 2 }{/tex}