Can you automate the drawing with a script? On X11, you can:
#!/bin/sh
# Position the pointer at the center of the dot, then run this script.
sleep 1
start=$(xdotool getmouselocation --shell)
eval $start
r=400
steps=100
down=0
for step in $(seq $((steps + 1)) )
do
# pi = 4 * atan(1)
new_x=$(printf '%s + %s * c(%s / %s * 2 * (4 * a(1)))\n' $X $r $step $steps | bc -l)
new_y=$(printf '%s + %s * s(%s / %s * 2 * (4 * a(1)))\n' $Y $r $step $steps | bc -l)
xte "mousemove ${new_x%%.*} ${new_y%%.*}"
if ! (( down ))
then
xte 'mousedown 1'
down=1
fi
done
xte 'mouseup 1'
xte "mousemove $X $Y"

Interestingly, you can abuse the scoring system (not manually, only with a script). Since the mouse *jumps* to the locations along the circle, you can just use very few steps and still get a great score because every step you make is very accurate – but the result looks funny:

🥴