ADD: The simplest workaround in Illustrator is at the end of this answer. Jump directly to it if you do not like elementary geometry nor methods which are either non-exact or need extra software.
There's an infinite number of possible curves which are tangential with 2 given circles, Actually there exists an infinite number of possible circle arcs ...
It seems you are using the transform effect to re-size and move each added stroke (It would be nice to see a screenshot of your transform effect panel).
It looks like you have decreased the vertical scale far more than the horizontal scale on your added strokes.
The only way to keep the slope (or angle) of your strokes the same as the original path is to ...
I guess your shape disintegrates as soon as your path is curved.
As a workaround make a horizontal shape and define it to be an art brush; drag it to the brushes panel to get the dialog opened:
Here it's applied to a vertical arc: