planning circuit

r = √(x² + y²)

Was this a more complicated question than it seems?

Are you trying to draw on a machine using steppers?

If so you would need a different approach because near to 90deg a big variation in x result in less than 1 step in y.

If the x increment is too small you may actually end up with a stepped arc.

The best is to draw the arc with a series of relative vectors of unequal length. actually selecting the best xy intersections on the path of the arc.

I am a bit capacity deprived at the moment and cannot get to my notes.

There are some potent formula on the web as well

drawing circles is far easier if you use a parametric approach.

for ang = 0 to 6.3 step 0.01;

x:= rad*cos(ang);

y:= rad*sin(ang);

plot(x,y);

next ang;

you will have to play with the step size to get a curve with no holes and offsets in the plot statement to move the circle where you want it on the screen. (And of course translate this into whatever programming language you are using...)