Question 68
Let $ABC$ be a triangle. We note $D$ and $E$ the respective media of the sides $AB$ and $AC$. Let $O$ be the center of the circumscribed circle of the triangle $ABC$. We note $K$ the point of intersection of the lines $(OE)$ and $(BC)$. We note $L$ the second intersection point of the line $(OD)$ with the circle circumscribed with the triangle $OKB$. We note $F$ The orthogonal projection of $A$ on the line $(KL)$. Show that points $D$, $E$ and $F$ are aligned.