Is $\mathbb{R}^2-B$ path connected where $B = \{(x,y) : x^2+y^2=1 \} \cup \{(x,y) : (x-2)^2 +y^2 \le1 \}$

Question

$B = \{(x,y) : x^2+y^2=1 \} \cup \{(x,y) : (x-2)^2 +y^2 \le1 \}$ is connected in $\mathbb{R}^2$ because $(0,1)$ is a limit point in both sets.

I am not sure how to continue beyond this to prove/disprove $\mathbb{R}^2-B$ is path connected