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:
