INMO 2004 Problem 4

Let $R$ denote the circumradius of a triangle $A B C ; a, b, c$ its sides $B C, C A, A B$; and $r_{a}, r_{b}, r_{c}$ its exradii opposite $A, B, C$. If $2 R \leq r_{a}$, prove that

(i) $a>b$ and $a>c$;

(ii) $2 R>r_{b}$ and $2 R>r_{c}$.