Show that the area lying in the region $x\geq 4$ and between the circle $x^{2}+y^{2}=32$ , the $x$-axis and the tangent drawn at the point $(4,4)$ on the circle is $4\left( 4-\pi \right)$ square units.
I tried plotting the concerned region, which I think is the area highlighted in green in the figure below. But I did not get the answer as $4\left( 4-\pi \right)$ square units.
AHE is 1/8 of the circle, ADE is a right triangle, so DHE is their difference.
EDF is the same as EDA and DHE is the same as DHG.
This should get you whatever you want.