I hope I have posted this in the correct forum.
I am a bit of a maths novice and I am having some difficulty calculating the final length of a line fixed between points A and B that is displaced by a circle of radius R.
The circle is at midpoint line AB (width W) and displaces line upwards a distance (D)
I need to calculate the minor arc length from D, w and R. I don't know the angle between the radii of the points of tangency, otherwise this would be easy
I have figured out how to calculate the minor arc length if I know the chord length and the sagitta (Hc) but these will depend on lengths D, w and R which will be known.
See the attched file for basic diagrams of the problem.
There must be some expression to calculate the minor arc length or even the chord length in this problem but I just can't figure it out.
Any help would be much appreciated.