First, I'm not a mathematician; just a retired grandpa who loves math...
Much easier to work out by taking a "small case"; let's make it 3 instead of 16;
we really need to concentrate only on quarter circle, as shown above.
GIVENS: Arc AY (your S/2), the radius (your D/2), and the number of points (your 16).
I'm naming them this way:
k = arc AY : assume 26
r = radius : assume 20
n = number of points : 3 as I indicated above
Calculations (p = pi) :
g = k/n : ~8.33 (corresponds to your g)
q = pr / 2 : ~31.42; quarter of circumference (or arc XY)
t = 90g / q : ~24.83 degrees; angle supporting each g (as example, angle AOB)
c = rSIN(t) : ~8.40; horizontal distance CY
b = rSIN(2t) - c : ~6.85; horizontal distance BC
a = rSIN(3t) - b - c : ~4.03; horizontal distance AB
I tested (to make sure!) on graph paper and all seems fine.
However, using n=16 will make it "long" if done as I'm showing,
so I presume you're also interested in a "quicker" way.
I'll try and do that in the next post.