JEE Math Practice Question

Let $$A=\left\{(x, y) \in \mathbb{R}^{2}: y \geq 0,2 x \leq y \leq \sqrt{4-(x-1)^{2}}\right\}$$ and $$ B=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: 0 \leq y \leq \min \left\{2 x, \sqrt{4-(x-1)^{2}}\right\}\right\} \text {. } $$. Then the ratio of the area of A to the area of B is

1. A.$$\frac{\pi}{\pi+1}$$
2. B.$$\frac{\pi-1}{\pi+1}$$
3. C.$$\frac{\pi}{\pi-1}$$
4. D.$$\frac{\pi+1}{\pi-1}$$