If I have the right to add that case where I think your method doesn't work, if not the moderator can delete that message ? I imagine a circle that I blowed up (inflate), like a balloon but it is a circle. The radius of the circle increases more and more but the center of the circle is fixed to the ground. I drew the device at start and at end:the original friction question has been settled
An enlargement to watch there is no friction:
I used your method (look at the dot of contact, they are at the same place):
I replace the circle at the center just to see the magenta length:
When I place the walls at the exact position, I need to count the movement of the magenta length. But there is no green length, the last drawing shows a difference of position of the dot of contact but look at the difference of length at the end of the walls, it is the same distance. I'm not sure at 100% there is no friction between the circle and the wall when I blow the circle, but the images seem to watch that.
The distance measure of friction is small but not exactly at 0, I measured: 0.03 but the distance calculated of the magenta length is 0.19, I can compare the lengths with the 2 following images at the same scale: