Question 85
Let $ABC$ be a triangle with acute angles, $\omega$ its circumscribed circle and $O$ the center of $\omega$. The perpendicular from $A$ compared to $(BC)$ intersect $(BC)$ in $D$ and $\omega$ in $E$. Let $F$ be a point on the $[AE]$ segment such as $2 \cdot FD = AE$. Let $\ell$ be perpendicular to $(OF)$ passing through $F$. Show that the line $\ell$, the line $(BC)$ and the tangent to $\omega$ in $E$ are concurrent.