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In the figure, O is the centre of the ci...

In the figure, O is the centre of the circle. `anglePOQ=90^@` .
The area of the shaded region is `126cm^2`. Find the radius of the circle.

Text Solution

Verified by Experts

Here , `anglePOQ=theta=90^@`
Area of the shaded region (i.e area of the segment PRQ) = `126 cm^2`
Area of segment PRQ `=r^2[(pitheta)/(360)-(sintheta)/2]`
`therefore126=r^2[(22xx90)/(7xx360)-1/2]`
`therefore126=r^2[(11)/(14)-1/2]" ...(sintheta=sin90^@=1)`
`therefore126 = r^2[(11-7)/(14)]`
`therefore126=r^2(4/(14))`
`thereforer^2=(126xx14)/4=441`
`thereforer=21 cm`
The radius of the circle is 21 cm
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