Question 138
Let $\omega$ be the incircle of triangle $ABC$, and let $\omega$ touch side $BC$ at $D$. Let $L$ be the second intersection of $AD$ with $\omega$. Let $K$ be the excenter of triangle $ABC$ inside angle $A$ (the $A$-excenter). Let $M$ be the midpoint of $BC$, and let $N$ be the midpoint of $KM$. Prove that $B$, $C$, $N$, $L$ are concyclic.