Not exactly mathematical notation (which labels points and hence makes naming "lines" easier), but let me try to understand your question.
You have the arc - i.e the circular part of the circle and the cord (I believe is the term), i.e. the bit that separates the arc.
I.e. you have an accurate description of the segment of the circle if I am not mistaken from your post.
Now at this point, your segment can rotate around the circle without any issues at all.
The radius as well as the height h will not change depending on where the segment will be located on the circle.
If you have the coordinates of one of the points or an angle however, you can start to draw triangles and work out the "unknown bits" step by step.
But if my understanding of your question is correct, and you have only a few lengths, then the answer is no.