I'm playing this addictive little compass and straight edge game: http://www.sciencevsmagic.net/geo/

I've been able to beat most of the challenges, but I can't construct a square in 8 moves.

To clarify a move is:

- Drawing a line
- Drawing a circle

Extending a line is not a move.

Lines can only be drawn to and from the root points and any intersections. Circles can be drawn with their center at any existing node and their edge must touch another.

My method for constructing the square in 9 moves is as follows:

- Draw circles from each point to the other, and the connecting line
- Use the intersections of the circles' edges to drawn a line perpendicular to the first
- Draw a smaller circle with its center at the intersection of the two lines and its edge touching the two root nodes.
- Connect the four points on the small circle's edge to form a square.

The end result looks like this:

I can't find a way to refine this method to get to eight moves, and I've failed at finding another method. Is it even possible?