Most of the calculations I know and can find can solve for the radius if the cord length is known or the angle is known along with the height of the arc segment. However I cannot find, nor figure out how to calculate the radius if only the arc segment and the height of the segment is known.
I have looked up several different methods on this and other site and the following are similar but not exactly what I am looking for.
- Calculate the radius of a circle given the chord length and height of a segment
- Calculating the height of a circular segment at all points provided only chord and arc lengths)
In CAD I can draw a arc like what is shown at (http://mathworld.wolfram.com/CircularSegment.html). If I fix the mid point at (0,0), the set the cord horizontal, then add a dimension the segment height (i.e. h=2") and then dimension the arc length (i.e. s=10"), the geometry is fully constrained. So I know there is a way to solve this.
If I reversed the inputs and had the arc length (s) known and the radius (R) known I can calculate the segment height but I am having trouble reversing the equation.