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<BC2 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.