Let ABC be an acute triangle with circumcircle ω and circumcenter O. The perpendicular from A to BC intersects BC and ω at D and E, respectively. Let F be a point on the segment AE, such that 2⋅FD=AE. Let l be the perpendicular to OF through F. Prove that l, the tangent to ω at E, and the line BC are concurrent.Proposed by Stefan Lozanovski, Macedonia JuniorBalkanshortlist2021geometryconcurrency