Another fine mess...Just to add some more goo to the stew, we might note the following:
As someone who spends a great deal of his time concerned with circular arcs, tangency, etc. while designing little things such as roads, I might suggest that the curves carved by a skier (including PSIman) making the appropriate progressive and continuous moves are not circular arcs of constant radius. To carve a constant radius circular arc would require an abrupt transition followed by a very static and rigid "park and ride."
In practice, we continuously increase or decrease edge angle, while at the same time adjusting many other parameters of our skiing. Some of the moves are conscious, some are not. Despite our best efforts, our shins are not perfectly parallel, and the two skis do not have exactly the same edge angle against the snow at the same instant.
We might also note that there is a range of edge angle in which the "pure carve" curve is very sensitive to the edge angle. A slight change in the edge angle can create a large change in the line.
The resulting curves are probably a complex hybrid combination of pieces of circular arcs, spirals, parabolas, and hyperbolas. The inside curve will be similar, but different from, the outside curve. Both the radii and the many various center points or focal points will be different. The inside curve will not be a simple exact offset of the outside curve.
As has been pointed out here already, there are a variety of things the skier can do to get the inside ski to lay down a line that appears roughly concentric with the trench carved by the outside ski. The fact that it isn't exactly concentric or parallel, and that neither line is a pure circular arc (and they don't need to be) gives the skier a good deal more latitude in adjusting the line of either ski and, in general, moving effectively.