Could it be a solution to draw a line between the horizontal one and the center point of the circle, then:
- Set the length of the line, so the distance between the circle and the horizontal line will be constant after moving each element
- Make it a construction line to avoid interfering with sketch fillings
Depending on your use case, Horizontal/Vertical and Perpendicular constraints could be a great addition between the horizontal and the construction line.
Or a simpler solution could be to select the line and the center point of the circle and set the distance between them.