[AO and OB segment are same as any other segment]. Each segment have same resistance r.

So I know that potential at C and E is same due to symmetry, B and D is same due to symmetry, and so on. Current in CB is same as ED and current in AO is same as OB and so on. But now what? Upper and lower part are not isolated because current in CO can go to OB and also go to OD .

I have solved this problem by brute force and answer is $ \frac45$r.