Let the circles C_1:|z|= r and C_2:|z-3-4 i |=5, z ∈ C, be such that C_2 lies within C_1. If z_1 moves on C_1, z_2 moves on C_2 and min |z_1-z_2|=2,…

Let the circles $\displaystyle \mathrm{C}_1:|z|=\mathrm{r}$ and $\displaystyle \mathrm{C}_2:|z-3-4 \mathrm{i}|=5, z \in \mathbb{C}$, be such that $\displaystyle \mathrm{C}_2$ lies within $\displaystyle \mathrm{C}_1$. If $\displaystyle z_1$ moves on $\displaystyle \mathrm{C}_1, z_2$ moves on $\displaystyle \mathrm{C}_2$ and $\displaystyle \min \left|z_1-z_2\right|=2$, then $\displaystyle \max \left|z_1-z_2\right|$ is equal to: