If in a triangle \(A B C, A D, B E\) and \(C F\) are the altitudes and \(R\) is the circumradius, then the radius of the circumcircle of \(\triangle \mathrm{DEF}\) is
(A) \(\frac{R}{2}\)
(B) \(\frac{2 R}{3}\)
(C) \(\frac{1}{3} \mathrm{R}\)
(D) None of these