Area of the largest circle that can be inscribed in a semicircle of radius $'r'$ units is

Question

$\begin{array}{1 1}(a) \; \sqrt{2}r^2 \;sq. units \\ (b) \; r^2 \; sq. units \\ (c)\;\frac{r^2}{\sqrt{2}} \; sq.units \\ (d)\; \frac{r^2}{2}\;sq. units\end{array}$