MathNet 2025-part-02 — 186 problems (EN–VI) Question 87

Let $ABC$ be a triangle whose incircle $(I)$ touches its sides $BC$, $CA$, $AB$ at $D$, $E$, $F$ respectively. The bisector of angle $BIC$ intersects $BC$ at $M$. The line $AM$ intersects $EF$ at $N$. Prove that $DN$ bisects angle $EDF$.