I have a circle with radius $R$ and center $(x,y)$ and I have the coordinate of a point; I want to find the minimum path between this point and the border of circle. Here is a picture of what I said:
Sorry if the picture is a disaster, I hope you will get the point.
On
Draw radius of the circle from the center to meet the circle at $(a,b)$ and draw a line from $(x,y)$ (your mentioned point outside of the circle) to $(a,b)$. Sum of these two connected lines are minimum if it is straight line, that is, the straight line from $(x,y)$ to $(a,b)$ must include the center as well; so it's the minimum distance!
You just need to find the distance between the point and the center of the circle and then subtract the radius from it.