Problem

Source: 2015 Saudi Arabia IMO TST III p2

Tags: geometry, arc midpoint, collinear



Let $ABC$ be a triangle and $\omega$ its circumcircle. Point $D$ lies on the arc $BC$ (not containing $A$) of $\omega$ and is different from $B, C$ and the midpoint of arc $BC$ . The tangent line to $\omega$ at $D$ intersects lines $BC, CA,AB$ at $A', B',C'$ respectively. Lines $BB'$ and $CC'$ intersect at $E$. Line $AA' $ intersects again circle $\omega$ at $F$. Prove that the three points $D,E,F$ are colinear. Malik Talbi