Then I asked her to draw a circle. Then I asked her to draw a line that touched that circle in only one point. She drew line #1 below (I added the numbering to make some distinctions here). Our conversation went something like this:
ME: Tell me why you decided to draw it that way.
HER: Well, cause it would only touch the circle in one point.
ME: What would happen if you continued your line?
HER: It would cross the circle on the other side.
ME: So would that work?
HER: I guess not....Well, I was thinking about this (draws line #2).
ME: Why did you decide not to draw that one?
HER: It just seems like it would touch the circle in more than one point.
ME: What if we zoomed in? (I drew the picture on the right)
HER: Hmmm...not sure. I still feel more certain that line #1 would only touch in one spot.