Question

In the given figure, if O is the center of the circle, PQ is a chord. \[\angle\] POQ = 90^°, area of the 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 

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

\[ \Rightarrow r^2 \left( \frac{3 . 14 \times 90° }{360°  } - \frac{\sin90° }{2} \right) = 114\]

\[ \Rightarrow r^2 \left( \frac{3 . 14}{4} - \frac{1}{2} \right) = 114\]

\[ \Rightarrow r^2 \times \left( 0 . 785 - 0 . 5 \right) = 114\]

\[ \Rightarrow r = \sqrt{\frac{114}{0 . 285}}\]

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

Thus, the radius of the circle is 20 cm.