Switch to outline mode (Ctrl+Y) and then manually align one of them until it looks good (make sure to zoom in).
▲ It will help to turn off all automatic snapping for this part
Now use the Rotate Tool (R) and with Smart Guides on (Ctrl+U to toggle on/off) click in the center of the circle to rotate around that point (your Smart Guides will snap to the center once you get close).
Follow the steps from this answer for rotating.
In the rotate dialog enter in the value
360/c (or 45° in your case)
c = amount of copies you want to have around your circle.
Now hit Ctrl+D a few times to fill it up
▼ Skip below mentioned and just follow steps from this answer for rotating.
Saved for historical significance of my backwards approach to this:
Now while holding down Alt (to copy the path) and Shift (to snap) you can Click+Drag the shape around your circle until 180° [See footnote]
Select both and while the Rotate Tool is still active, hit Enter
I thought you could simply place the pointer where you want to rotate around and then use something like Transform Effects to rotate and place all the copies - or even the regular rotation panel, but when I tried that it reset my rotate-around-point.
Therefore, you first have to make a copy 180°, that will set the center point where you want it.
Edit: there is a way