Is there any transformation that can map 3 or 4 circles to concentric circles?

Question

I am searching two transformations that can map circles into concentric circles.

1) a transformation maps $C_1(d,r_1)$, $C_2(0,r_2)$ and $C_3(0,r_3)$ into $C_1(0,r_1')$, $C_2(0,r_2')$ and $C_3(0,r_3')$, where $d+r_1<r_2<r_3$, I wish mapped circles' radius satisfy $r_1'<r_2'<r_3'$;

2) a transformation maps $C_1(d,r_1)$, $C_2(0,r_2)$, $C_3(0,r_3)$ and $C_4(0,r_4)$ into $C_1(0,r_1')$, $C_2(0,r_2')$, $C_3(0,r_3')$ and $C_4(0,r_4')$, where $d+r_1<r_2<r_3<r_4$, I wish mapped circles' radius satisfy $r_1'<r_2'<r_3'<r_4'$.

Are there exist these transformations?

Thanks,

Tang Laoya