Your design requires you to constrain a part with a spherical face to another part with a circular edge. But when you went to apply a tangent constraint between the spherical face and the circular edge you realized that Inventor doesn't allow you to select edges for a tangent constraint.
Solution:
Although you can't apply a tangent constraint in this case, you can use other Inventor tools to achieve the same result.
In this case, my two parts are already constrained along the center axis of each, so that the rod with the hemispherical face slides free toward the circular edge. So what I'll do next is create a Contact Set to be used with the Contact Solver tools. This allows me to slide the rod in until it contacts the other part, and it will stop at the exact point that the hemispherical face contacts the circular edge.
I do this by selecting both parts and then right-clicking and choosing Contact Set:
Then I'll go to the Inspect tab and turn on the Contact Solver:
Now that the Contact Set has been created and the Contact Solver has been enabled, I can drag the rod toward the other part until it touches, at which point it will stop and the hemispherical face will be touching the circular edge of the hole:
So now my two parts are constrained perfectly:
Keep in mind that it's best to disable the Contact Solver when not specifically finding contacts between parts, because it might otherwise impact performance in a negative way as Inventor attempts to solve contact relationships while you drag other parts around in typical constraint and assembly tasks. Here's a link to another tip along with a video dealing withe the Contact Solver.
Also, remember that when you enable the Predict Offset and Orientation check-box it will stay on until you turn it back off. This can often be a source of confusion if you forget that you've turned it on, because your parts will constrain at their current offset rather than with a zero offset, as is more typical.
