## f(t): Help Me With Some Algebra

f(t): Help Me With Some Algebra

Given a chord AB and the intercepted arc S, is it possible to find radius r algebraically? (problem stated at f(t)) The consensus there seems to be no, due to the transcendental nature of sin(x).

But I find it interesting that r could be constructed with a compass and straightedge. However, I feel like I’m cheating with Geogebra since I had to place C in order to draw arc S. So I really wasn’t given S; I picked one based on C. Circular logic! (that’s a little math joke … ha ha ha.)

Update: http://www.mathforum.com/dr.math/faq/faq.circle.segment.html#1 Dr. Math has a nice page about solving circles given arbitrary parts. They reinforce the idea that this is a problem with numerical-only solution. Their solution involves Newton’s Method, something I myself am not very well versed in these days!