Problem

Source: Bulgarian Autumn Tournament 2023, 10.2

Tags: geometry



Given is an acute triangle $ABC$ with circumcenter $O$. The point $P$ on $BC$ such that $BP<\frac{BC} {2}$ 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.