%!

/pi 3.141592653589 def

% the parametrization of the circle of radius r is (x + R cos(t), y + r sin(t))
% the velocity at t=0 is (0, r) and the parameter difference is pi/2, so the control point is (pi/6)(0, r)

% x y r 
/build-circle { 3 dict begin
/r exch def
/y exch def
/x exch def
/d pi 6 div r mul def
x r add y moveto
x r add y d add
x d add y r add
x y r add curveto
x d sub y r add
x r sub y d add
x r sub y curveto
x r sub y d sub
x d sub y r sub
x y r sub curveto
x d add y r sub
x r add y d sub
x r add y curveto
closepath
end } def

gsave
currentlinewidth 10 mul setlinewidth
1 0.7 0.7 setrgbcolor
newpath
100 100 100 0 360 arc 
stroke
grestore

newpath
100 100 100 build-circle 
stroke