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# A diagram shows a circle centre o,radius 9cm.The tangent to the circle at A meets OB produced at T.The area of the sector OAB is 24cm^2. ?

Calculate the area of the triangle OAT..

Helppppppp pleasssssss

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- King LeoLv 74 months agoFavorite Answer
Area of a sector of radius r and angle θ

Area = ½r²θ

24 = ½(9)²θ

∴ θ = 16/27

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Tangent ratio

tanθ = ( AT ) / ( OA )

∴ AT = ( OA ) tanθ

AT = 9 tan(16/27)

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Area of Triangle OAT

Area = ½ ( OA )( AT )

= ½ ( 9 )9 tan(16/27)

= 27.27 cm²

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