Question 48
Let $ABC$ be a triangle and $C$ its circumcircle. The point $D$ lies on the arc $BC$ of $C$ and is different from $B$, $C$ and the midpoint of $BC$. The tangent line to $C$ at $D$ intersects the lines $BC$, $CA$, $AB$ at $A'$, $B'$, $C'$, respectively. The lines $BB'$ and $CC'$ intersect at $E$. The line $AA'$ intersects again the circle $C$ at $F$. Prove that the points $D$, $E$, $F$ are collinear.