I'm trying to find $r>0$ such that there is a Mobius transformation between $\left\{z\in\Bbb C:r<|z|<1\right\}$ and the domain bounded by $|z-1/4| = 1/4$ and $|z| =1$. I have no clue what $r$ should be. Any hint for this problem?
2026-03-29 16:47:54.1774802874
Mobius transformation from an annulus to a bounded reigon
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