Question

In figure $segAB$ is a chord of a circle with centre $P$. If $PA=8cm$ and distance of chord $AB$ from the centre $P$ is $4cm$, find the area of the shaded portion.
$(\pi =3.14,\sqrt{3}=1.73)$

Answer 1

Area of shaded region $=$ Area of segment $PAB-$Area $\left(△PPB\right)$

In $△PMA,\cos \theta =\frac{4}{8}=\frac{1}{2}\Rightarrow Q={60}^o$

$\Rightarrow$ Area of segment $=\frac{\pi r^2}{360}\times 120\frac{\pi r^2}{3}$

$\Rightarrow$ Shaded area= $\frac{\pi r^2}{3}\times \frac{1}{2}\left(AB\right)\left(4\right)$

$=\frac{AM}{AP}\Rightarrow AM=\frac{3}{2}\times 8=4\sqrt{3}\Rightarrow AB=8\sqrt{3}\Rightarrow$ Area $=\pi \left(64\right)+16\sqrt{3}=94.68c{m}^2$