Describe the position of $w_0=\frac{(|z_0|+r)+R}{2}\cdot\frac{z_0}{|z_0|}$ w.r.t. $B_R(0)$ and $B_r(z_0)$

Question

I am working with two circles $B_R(0)$ and $B_r(z_0)$ and want to describe the position of the point given by $$w_0=\frac{(|z_0|+r)+R}{2}\cdot\frac{z_0}{|z_0|}.$$ First I would like to know whether my assumption where the point is, is correct and how you would describe its position. Here is my most beautiful Paint picture for this matter