Question 11
Let $I$ be the incenter of triangle $ABC$. Let $R_A$, $R_B$ and $R_C$ be the radii of the circumcircles of triangles $BIC$, $CIA$ and $AIB$, respectively, and $R$ be the radius of the circumcircle of triangle $ABC$. Prove that $R_A + R_B + R_C \le 3R$.