There have been several posts about the lack of control in SU over snapping points. Other CAD systems allow much finer control. What that means is that you often have to zoom in really close to ensure you are selecting the point you want, which is a faff. I don’t know why it wasn’t letting you snap to an intersection point on the circle. That does seem strange. However, to avoid all the zooming in and out and making sure you land where you want, here is what I often do. Draw the line from the point you want outside the circle to a random point inside the circle that is not a vertex but lies along your construction line. Then delete the section of line inside the circle. Does that work? (As you haven’t uploaded your file, I can’t check).