Given an acute triangle
with
. Point
is the incenter, and
the circumradius. Point
is the foot of the altitude from vertex
. Point
lies on line
such that
, and
separates
and
. Lines
and
meet sides
and
at
respectively. Let
.
Prove that
.
Author: Davoud Vakili, Iran
%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
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