Quandaries and Queries
Given only the length of an arc (72) & the length of its cord (71), how to find the radius?
Unfortunately there isn't a nice answer to your question. I drew a diagram and labeled various parts.
A is the midpoint of the chord so |AB| = 71/2. I let theta be the angle at the center of the circle subtended by the arc. Theta is in radians. Triangle ACB is a right triangle so
The length of the arc subtended by the angle theta is 72 so
Hence, substituting into the first equation and simplifying I get
The best you can do now is use some numerical method to approximate r.