okay okay okay - forget everything i wrote before. here's the deal:

let "d" be the actual distance between the bb and hub centers, "r1" be the cog diameter and "r2" be the chainring diameter. than:

alpha = arcsin((r2-r1)/d)
straight lengths = [d^2 - (r2 - r1)^2]^(1/2)
cog arc = r1*(pi - 2*alpha)
chainring arc = r2*(pi + 2*alpha)

i finally realized the significance of the symmetry. sorry for all the confusion.