Got it, applying a vertical and then horizontal constraint to the center point of the circle, and the rectangle worked.
For context: For a two-part pin-and-socket clip, I copied an ellipse for the pin feature on part A and wanted to center it at the midpoint between projected geometry on part B to create the socket feature.
In AutoCAD, after copying the geometry, I would use Move > select geometry > shift+right click Geometric Center for the move point > shift+right click Mid Between 2 Points to place
For Inventor, after copying the geometry, applying a vertical then horizontal constraint seems to achieve the same result, placing the copied geometry between two selected points
The better approach (fewer clicks) I realize now (probably obvious to most), just copy the part file for part A, relabel it, then edit the extrusion for the pin feature to create the socket. Don't know if it would be better still to just make it in one part file ..?
Thanks Kacper for the tip of turning to constraints as opposed to the move command!