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Let in a circle,radius r,centre O, an ar...

Let in a circle,radius r,centre O, an arc AB of length l subtends an angle `theta` radian at centre. Show that : (1) `l=rtheta` (2) Area of sector OAB=`1/2r^2theta` What are the corresponding formula if `/_AOB=theta` degree?

Text Solution

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1) Area of length=`2pir`
(when `theta=2pi)`
arc length=`rtheta'`
`l=rtheta'`
2)Area of sectorOAB
`2pi=pir^2`
`1=(pir^2)/(2pi)`
`theta=(pir^2)/(2pi)theta`
...
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