I think it's important that they are talking about lines not line-segments. By definition, lines extend to infinity in both directions. But I agree, the wordi

I think it's important that they are talking about lines not line-segments. By definition, lines extend to infinity in both directions. But I agree, the wording is still confusing. I would have worded it more like "if three lines pass through the same point and the edge of a circle, then the point is the center of the circle and the lines lie along the radii of the circle."