MathNet 2019-part-05 — 184 problems (EN–VI) Question 15

Let $ABC$ be an acute triangle such that $AB \lt AC$. Let $I$ be the incentre of the triangle $ABC$, and let the incircle touch the side $BC$ at $D$. The line $AD$ crosses the circle $ABC$ again at $E$. Let $M$ be the midpoint of the side $BC$, and let $N$ be the midpoint of the circular arc $BAC$. The line $EN$ crosses the circular arc $BIC$ at $P$. Show that the lines $AD$ and $MP$ are parallel.

Ukraine National Olympiad, 2016