Attach vertex to a circle with a line? I have a basic circle with lets say 20 vertices.
I then do a ctrl+right click to place a vertex somewhere outside the circle.
I then select the vertex outside the circle, hold shift, select a vertex on the circle and hit f.
And nothing happens.
I can ctrl+right click around and shift select and f lines all day. But can't seem to get the vertex to join the circle with a line.
In curves, the vertices cannot be linked to more than two segments, curves cannot be forked or bifurcated.

To create such shape you would need to add a new disconnected curve segment and place it on top of an existing one.