Problem source

The line $y=d\,$, where $d>0\,$,
intersects the circle $x^2+y^2=R^2$ at $G$ and $H$. Show
that the area of the minor segment $GH$ is equal to
\begin{equation}
R^2\arccos \left({d \over R}\right) -d\sqrt{R^2 - d^2}\;.
\tag
{$*$}
\end{equation}

In the following cases, the given line intersects the
given circle. Determine how, in each case, the expression $(*)$ should be modified
to give the area of the minor
segment.

  
\begin{questionparts}
\item
Line: $y=c\,$; \ \ \ circle: $(x-a)^2+(y-b)^2=R^2\,$. 
\item
Line: $y=mx+c\, $;  \ \ \  circle: $x^2+y^2=R^2\,$. 

\item
Line: $y=mx+c\,$; \ \ \ circle: $(x-a)^2+(y-b)^2=R^2\,$.
\end{questionparts}