I agree with Ken's answer (although i got it in a slightly different form)
S = (3*sqrt(3) + 2*sqrt(2))R = Ken's answer since 3*sqrt(3) = 6*Sin120
R = S / (3*sqrt(3) + 2*sqrt(2))
and BD = S * sqrt( (237 - 40*sqrt(6)) / 361)
The solution for finding R in terms of S basically boils down to finding the sides of 3 right triangles for those who are looking for a hint. (Remember the special stuff about tangents to circles? yeah...) And to find BD, cosine law
Soo... do I win a prize too?
Anthony.