Question

In the figure, if O is the center of the circle, PQ is a chord $\angle POQ={90}^{\circ }$ area of the shaded region is $114$ cm, Find the radius of the circle

Answer 1

$\angle POQ=\theta ={90}^{\circ }$
Let the radius of the circle be r cm.
Area of the shaded region = Area of the segment $PRQ=114c{m}^2$

$[\therefore r^2(\frac{\pi \theta }{360°}-\frac{\sin \theta }{2})=114]$

$[\Rightarrow r^2(\frac{3.14\times 90°}{360°}-\frac{\sin 90°}{2})=114]$

$[\Rightarrow r^2(\frac{3.14}{4}-\frac{1}{2})=114]$

$[\Rightarrow r^2\times (0.785-0.5)=114]$

$[\Rightarrow r=\sqrt{\frac{114}{0.285}}]$

$[\Rightarrow r=\sqrt{400}=20cm]$

Thus, the radius of the circle is $20cm$.