Question

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

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

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

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

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

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

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

Thus, the radius of the circle is 20 cm.