Question 5
Let $ABC$ be a triangle inscribed in circle $(O)$, with its altitudes $BH_b$, $CH_c$ intersecting at orthocenter $H$ ($H_b \in AC$, $H_c \in AB$). $H_b H_c$ meets $BC$ at $P$. Let $N$ be the midpoint of $AH$, $L$ be the orthogonal projection of $O$ on the symmedian with respect to angle $A$ of triangle $ABC$. Prove that $\angle NLP = 90^\circ$.