As shown in the figure, the pattern inside square $ABCD$ comes from the ancient Chinese Tai Chi diagram. The black and white parts in the inscribed circle of the square are symmetric with respect to the center of the square. If a point is randomly selected from the square, the probability that it falls in the black part is
A. $\frac{1}{4}$
B. $\frac{\pi}{8}$
C. $\frac{1}{2}$
D. $\frac{\pi}{4}$