Question 27
Let $R$ denote the circumradius of a triangle $ABC$; $a, b, c$ its sides $BC, CA, AB$; and $r_{a}, r_{b}, r_{c}$ its exradii opposite $A, B, C$. If $2R \leq r_{a}$, prove that
(i) $a \gt b$ and $a \gt c$;
(ii) $2R \gt r_{b}$ and $2R \gt r_{c}$.
(i) $a \gt b$ and $a \gt c$;
(ii) $2R \gt r_{b}$ and $2R \gt r_{c}$.