Aligning shape edges to one another

I’m trying to align an angled line to the edge of a circle so that it’s essentially snapped to the circle’s tangent. All I can seem to do is snap the edge of the line’s “outline box” to the edge of the circle and only when I’ve enable “snap to edges”, this obviously doesn’t position the line itself anywhere near the circle. I’m assuming there’s a simple trick I’m missing?

Snapping on object guides just plain doesn’t work, unfortunately.