How do I center one object relative to a folder full of objects?

I have two folders. They each contain a half-circle that visually combine to make a full circle. 

I have another square shape that is outside of those two folders. I would like to center this square shape to the "circle" made up of the two aforementioned folder. So visually the result should be a square perfectly centered to the (visual) shape of the circle. 

If I were using Photoshop, I would put both folders containing each half-circle into a parent folder. Then Photoshop treats those individual pieces a whole for purposes of alignment and centering. Illustrator seems not to do this unless there's some toggle or something I need to apply. 

Thanks in advance for any assistance.