If the diagonal BC passes through center of the circle, then the area of the shaded region in the given figure is
\begin{align*} a)\quad &\dfrac{a^2}{2(3-\pi)}\\
b) \quad &\dfrac{a^2}{\frac{\pi}{2}-1}\\
c) \quad &2a^2(\pi-1)\\
d) \quad &\dfrac{a^2}{2(\frac{\pi}{2}-1)}
\end{align*}
Hint: What is the area of the circle? If the line $BC$ passes through the center of the circle, what area is on either half of the line? And finally, what is the area of the triangle?