Here is a picture of my problem: 
"m" (not sure if there is a name for this) is known and the arc length between D and B is known. BC is tangent to the circle at point B. What is the radius "r" (or chord length BD or angle BAD)?
I can work this out graphical for m = 2.1m and arc length BD = 5m but I don't have a formula for it yet.
Sorry, first time poster and on the site... I came across this problem at work and I have been unable to solve it as my algebra is rusty an my Googlefoo failed me. I looked through about 40 related questions on this site and didn't find the answer, but it looks like there are lots of Mathematicians here which should be able to solve it.
Any help or a link to the right page would be great, Cheers!