Greetings from Greece and Congratulations for keeping Dr.Geo alive.
Trying to make a regular hexagon from a circle , it'd be helpfull to make an arc clockwise.
Otherwise i think we must use complete circles.
I noticed the same in other interactive geometry software too.
So reading the construction my mind lingered on the phrase ' ...swing a small arc crossing the circumference of the circle.' and i thought if that kind of movement could be usefull in simulating in Dr.Geo..
Also i uploaded an image of contstucting a hexagon on a given segment , and again the 'compass swinging' seems usefull.
Nevertheless, given the dynamic nature of the sketch, it is better to use a complete circle, otherwise when you drag around some points, the arcs may not intersect any more. Of course, visually it is not as nice as using only arcs ;-)