Školjka

%V0 Given an acute triangle $ABC$ with $\angle B > \angle C$. Point $I$ is the incenter, and $R$ the circumradius. Point $D$ is the foot of the altitude from vertex $A$. Point $K$ lies on line $AD$ such that $AK = 2R$, and $D$ separates $A$ and $K$. Lines $DI$ and $KI$ meet sides $AC$ and $BC$ at $E,F$ respectively. Let $IE = IF$. Prove that $\angle B\leq 3\angle C$. Author: Davoud Vakili, Iran