I rediscovered the arclength of a circular segment of a circle, created by a chord!

arclength = radius * Theta = radius * 2 * arcsin((sqrt(dx*dx + dy*dy))/(2*radius))

This should be very useful.

The equation is here, with delta_x and delta_y substituting for the chord length, by pythagorus:

https://en.wikipedia.org/wiki/Circular_segment

- Brian