First, I'm not a mathematician; just a retired grandpa who loves math...

Code:

Y(0,r)
C
B
A
O(0,0) X(r,0)

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.