MathNet 2014 Question 31

Let $\triangle ABC$ be a triangle. The external and internal angle bisectors of $\angle CAB$ intersect side $BC$ at $D$ and $E$, respectively. Let $F$ be a point on the segment $BC$. The circumcircle of triangle $\triangle ADF$ intersects $AB$ and $AC$ at $I$ and $J$, respectively. Let $N$ be the mid-point of $IJ$ and $H$ the foot of $E$ on $DN$. Prove that $E$ is the incenter of triangle $\triangle AHF$.

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