Question 170
Let $ABC$ be a triangle whose incircle $(I)$ touches $BC$, $CA$, $AB$ at $D$, $E$, $F$, respectively. The line passing through $A$ and parallel to $BC$ cuts $DE$, $DF$ at $M$, $N$, respectively. The circumcircle of triangle $DMN$ cuts $(I)$ again at $L$.
1. Let $K$ be the intersection of $NE$ and $MF$. Prove that $K$ is the orthocenter of the triangle $DMN$.
2. Prove that $A$, $K$, $L$ are collinear.
1. Let $K$ be the intersection of $NE$ and $MF$. Prove that $K$ is the orthocenter of the triangle $DMN$.
2. Prove that $A$, $K$, $L$ are collinear.