Problem

Source: MEMO 2017 T6

Tags: geometry



Let ABC be an acute-angled triangle with ABAC, circumcentre O and circumcircle Γ. Let the tangents to Γ at B and C meet each other at D, and let the line AO intersect BC at E. Denote the midpoint of BC by M and let AM meet Γ again at NA. Finally, let FA be a point on Γ such that A,M,E and F are concyclic. Prove that FN bisects the segment MD.