Question 8
An acute-angled triangle $ABC$ is given, where $AB \lt BC$. Its incircle with the centre in point $I$ is touching the side $BC$ in point $K$. The line $AK$ intersects a second time the circumscribed circle of triangle $ABC$ in point $T$. Let $M$ be the midpoint of $BC$, and $N$ be the midpoint of arc $BAC$ of the circumscribed circle of triangle $ABC$. Line segment $NT$ intersects the circumscribed circle of triangle $BIC$ in point $P$. Prove that $PM \parallel AK$.