SHARYGIN 2018 Problem 20

Let the incircle of a nonisosceles triangle $ABC$ touch $AB$ , $AC$ and $BC$ at points $D$ , $E$ and $F$ respectively. The corresponding excircle touches the side $BC$ at point $N$ . Let $T$ be the common point of $AN$ and the incircle, closest to $N$ , and $K$ be the common point of $DE$ and $FT$ . Prove that $AK||BC$ .