12. If the set $A=\{(x, y)|y=-| x |-2\}, B=\left\{(x, y) \mid(x-a)^{2}+y^{2}=a^{2}\right\}$ satisfies $A \cap B$ $=\varnothing$, then the range of real number $a$ is
12. $-2 \sqrt{2}-2<a<2 \sqrt{2}+2$ Hint: Set $A$ represents two rays: $y=-x-2, x \geqslant 0, y=x-2, x<0 . a=0$ when, $B$ represents a point $(0,0) ; a \neq 0, B$ represents a circle with center $(a, 0)$ and radius $|a|$, use the fact that the circle and the lines are disjoint.