Not possible. We do not have the distance relationships for the nine most-central green points in regard to distance from center point to green point on the circle. For example, how does AF relate to FK ? The point F is not the mid point of those. It may LOOK like it, but we are not given that specifically.
... On the other hand, if we can take it that F is a midpoint of AK, then we have something. We might assume the circle is r radius so we have x^2+y^2=r^2, and if we just assign a number or know a number for r, then from the center of the circle, we can read x or y coordinates and calculate the other coordinate. Then we have whatever red point on the circle we want.
Imagine r=1, and KC=1, and KL is 1/2. You then have x=1/2. You could find y.
y^2+(1/2)^2=1