Question 138
Bisector of the angle $\angle ABC$ of the triangle $ABC$ intersects the circumcircle of triangle $ABC$ at the point $K$. Point $N$ belongs to the segment $AB$ and $NK \perp AB$. Let $P$ be a midpoint of the segment $NB$. Consider the line through $P$ that is parallel to $BC$ and intersects line $BK$ at the point $T$. Prove that the line $NT$ passes through the midpoint of the segment $AC$.
(Nagel Igor)
(Nagel Igor)