I would draw a temporary vertical edge down from the horizontal one and then temporarily erase the horizontal edge. Then use the arc tool from the end of the vertical edge to the circle and look for the “tangent to edge” tooltip. The temporary vertical gives the arc tool the desired target for tangent at that end. Then erase the vertical edge and redraw the horizontal one to clean up.
Here is another method, more elaborate that @slbaumgartner 's because I wasn’t sure how Steve’s method determines the endpoint of the arc such that it is on a radius from the circle and exactly tangent to the circle.
Start with the basic setup, not including all of the geometry in your model.
Add a guide point (with horizontal leader line) starting at point A (the right-most end point of the short horizontal edge just below the circle) and of length that equals the radius of the circle.
Draw a temporary vertical edge, of arbitrary length, starting at the new guide point from step 2. This edge will help draw an arc that is tangent to the temporary edge.
Draw a temporary arc (using the default two-point arc tool) starting at the guide point added in step 2, and ending at the center of the circle (who’s center is indicated using the Find Center function). This arc obviously crosses the circle and thus cuts one of its segments at some arbitrary point. If that is not desired, these steps could be done in a group superimposed on the original geometry.
Find the new center of the temporary arc. Use the plain Arc tool (Command-J on a Mac) to draw the final desired arc. Start this final arc at the new center point. Click the first end of the arc on the right-most end of the horizontal edge below the circle. Click the second end of the arc at the center of the circle - this ensures that the final arc is exactly tangent to the theoretical circle.
You probably want to re-draw the circle at this point, or draw a new arc in place of the circle, such that one end-point of the new arc is exactly at the end-point of the arc added in step 5.
