my build from the start

[h4ppy-chris]

thanks peter star man, added it to the post :-)

[Jonathan]

Ahh, now I understand the question! You wanted *diameter* not circumference at stated in your post.

It's just cos(30)...

Let x be side length of the triangle the three points form (i.e 35mm).

(see diagram)

Draw in lines on triangle that bisect the angles. So we've now got a smaller triangle with one side length x/2, and we know the angle indicated is 30 degrees, since it's an equilateral triangle and we've bisected the corner angle.

cos(30)=(X/2)/r
r=X/2/cos(30)
r=17.5/cos(30) = 20.2072594...
(since d=2r, d=X/cos(30))

Incidentally to help remember it cos(30) is just sqrt(3)/2 = 0.866025...
Hope that helps. You can get the other PCDs using similar methods. 4 is half root 2.