Suppose we have a circle stroke that is 100px in width. We now want to change it so that the center left side has a stroke with of 50px and the width should increase symmetrically such that when the top and bottom sides reach the right half of the circle the width of the top and bottom left half is 100px?
Also, this might be the same technique, but suppose the center point of the right side of the circle stroke has a width of 100px and we want this to decrease symmetrically and continuously until we reach the left side center point which has a 50px width.
Set the Display Units in the Document Properties (on the Page tab) to pixels. And set up some vertical guides to help you measure the stroke widths.
The following method uses two circles to do this. It’s easier and quicker than using a PowerStroke path effect for varying stroke widths – but that is another way you could do it.
Draw the larger circle first. Hold down Ctrl as you click and drag to constrain the proportions of the circle. Use snapping so that everything lines up with the guides.
Then draw the smaller circle.
Using snapping, move them into the correct position
Select both circles, then click Path > Difference (Shortcut: Ctrl+-).
Set a fill and no stroke.