@tomasplasil You have the right mindset when trying to get vertices and edge lining up. There’s however more convenient ways to do so. First I would do as you did: to start with a circle and inset it (either fill in the face and inset, or extrude and scale toward its center). Then I’d suggest to add loop cuts (ctrl+r), that way the start and end vertices of each segment are connected. Finally, when you start editing the segment, try not to change the edges that hold the segment.
That way, when you duplicate and rotate the segment everything will be exactly at the correct spot.
I hope this helps, I’ll try not to give you the “answer” but rather guidelines so you can practice!
/Thibaut.