Question

In the given figure, if O is the centre of the circle, PQ is a chord. $\angle$POQ = 90^°, area of shaded region is 114 cm² , find the radius of the circle.
($\mathrm{\pi }$ = 3.14)

Answer 1

∠POQ = θ = 90º

Let the radius of the circle be r cm.

Area of the shaded region = Area of the segment PRQ = 114 cm²

$$\begin{gathered} \therefore r^2\left(\frac{\mathrm{\pi }\theta }{360°}-\frac{\sin \theta }{2}\right)=114 \\ \Rightarrow r^2\left(\frac{3.14\times 90°}{360°}-\frac{\sin 90°}{2}\right)=114 \\ \Rightarrow r^2\left(\frac{3.14}{4}-\frac{1}{2}\right)=114 \\ \Rightarrow r^2\times \left(0.785-0.5\right)=114 \\ \Rightarrow r=\sqrt{\frac{114}{0.285}} \\ \Rightarrow r=\sqrt{400}=20\mathrm{cm} \end{gathered}$$
Thus, the radius of the circle is 20 cm.