Tuff math problem with easy intuitive solution.

[kedaman]

Sorry for not being too clear, my formulas are supposed to work with polygons with P corners.

Angle from center between points: a=2pi/pradius (I think this should be a = 2*pi/P for radians, or 360/P for degrees), but since you do not use it anywhere, I guess it does not matter.

I was to use that angle but dunno why i typed that other formula, maybe i had it for another angle that i abandoned later. 50/sin(a/2) is exactly what it should be

__50______
\    |
 \   |
  \  |
 r \ |
    \| <- a/2
     C

Also the radius shouldn't be there either, in the formla to get a.

   __
    /|
 Vt/   _____
  /___/     \_____
_/______\_________\
 \b     /
  \  
   \Vc
   _\
     \
      \
       \C

Vt and Vc here are the speed components (should be right angled) in tangential direction and centripetal direction. the angle inside cos, is not a, as you see, it's b = (pi/2-a) So i could as well write the formula:
V=sin(a/2)
I think the confusion is that i used the b angle all the time, which i got another formula for, i