Question 130
Given an acute triangle $ABC$ with circumcenter $O$. The point $P$ on $BC$ such that $BP \lt \frac{BC}{2}$ and the point $Q$ is on $BC$, such that $CQ = BP$. The line $AO$ meets $BC$ at $D$ and $N$ is the midpoint of $AP$. The circumcircle of $(ODQ)$ meets $(BOC)$ at $E$. The lines $NO$, $OE$ meet $BC$ at $K$, $F$. Show that $AOKF$ is cyclic.
(Alexander Ivanov)
(Alexander Ivanov)