Bonjour @rpajounia
Here is a very simple solution with an LSP file.
You have to click the circle, the point on the circle to define the start of the distance and the desired distance.
A small circle will be drawn at the given distance from the starting point counterclockwise.
This is a very simple first version to understand your request, I can work to improve it...
The point for the start of distance must be on the circle, I have not done a snag test
Amicalement
(defun c:disc ( / dis ent pt pt2)
(setq ent (car (entsel"\nCircle ?\n")))
(setq pt (getpoint "\nStart point for distance ?\n"))
(setq dis (getreal "\nDistance for desired point\n"))
(setq pt2 (vlax-curve-getpointatdist ent
(+ dis (vlax-curve-getdistatpoint ent pt))))
(command "_circle" pt2 0.1)
)