8. In the following right-angled triangle $A B C, \triangle C=B C=1$ and $D E F$ is an arc of a circle with center $A$. Suppose the shaded areas $B D E$ and $C E F$ are equal and $A D=\frac{x}{\sqrt{\pi}}$. What is the value of $x$ ?
(A) 1;
(B) 2 ;
(C) 3 ;
(D) 4 ;
(E) 5 .
8. Ans: (B)
Since the area of sector $A D F$ and $\triangle A B C$ are equal, we have
$$
\frac{1}{2}\left(\frac{x}{\sqrt{\pi}}\right)^{2} \frac{\pi}{4}=\frac{1}{2} \text {. }
$$

The result follows.