Mathematics

Problem

Let

A = \{(x, y) \in \mathbb{R}^2 : y \ge 0, 2x \le y \le \sqrt{4 - (x-1)^2}\}

and

B = \{(x, y) \in \mathbb{R} \times \mathbb{R} : 0 \le y \le \min\{2x, \sqrt{4 - (x-1)^2}\}\}

Then the ratio of the area of A to the area of B is (A)

\frac{\pi - 1}{\pi + 1}

(B)

\frac{\pi}{\pi - 1}

(C)

\frac{\pi}{\pi + 1}

(D)

\frac{\pi + 1}{\pi - 1}