Here's a module that takes a slice of one side of a cylinder.

Two questions:

1. I'm just getting started with composing things in modules.  Is
   the approach reasonable, or is there a better way to chop off
   the unused part of the cylinder?

2. This module specifies the radius and a percentage of the circle
   to keep.  I would rather specify:

   - thickness (as is now)
   - length of chord
   - distance from chord to edge of cylinder
   

   If someone could give me a clue as to deriving the location and
   radius of the cylinder from the chord length and height, I would
   appreciate it!

module arc(thick, rad, percent) {
translate([thick/2,0,-rad+(2radpercent)]) {
rotate([0,-90,0]) {
intersection() {
translate([2rad(1.0-percent),0,0])
cube([2rad,2rad,thick], center=true);
cylinder(thick, r=rad, center=true);
}
}
}
}
arc(5, 40, .1);

When you speak of the chord of a cylinder, I hope you mean the chord of a
circle created by a perpendicular slice of the cylinder. If you add in the
angle of the slice, the math goes way out of control.

On that note, there's a series of answers located here:

Various methods to calculate circle radius
https://math.stackexchange.com/questions/564058/calculate-the-radius-of-a-circle-given-the-chord-length-and-height-of-a-segment

If the multitude of answers presented in math.stackexchange.com doesn't work
for you, give this one a try:

More options for chord calculations http://bfy.tw/CrMl

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https://softsolder.com/2013/08/02/making-finger-grip-dents-the-chord-equation/

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