JBMO-SL 2021 G3

Let $ABC$ be an acute triangle with circumcircle $\omega$ and circumcenter $O$ . The perpendicular from $A$ to $BC$ intersects $BC$ and $\omega$ at $D$ and $E$ , respectively. Let $F$ be a point on the segment $AE$ , such that $2 \cdot FD = AE$ . Let $l$ be the perpendicular to $OF$ through $F$ . Prove that $l$ , the tangent to $\omega$ at $E$ , and the line $BC$ are concurrent.

Proposed by Stefan Lozanovski, Macedonia