Question 100
Let $ABCD$ be a cyclic quadrilateral and let $\mathcal{K}$ be its circumcircle. Denote the intersection of the lines $AB$ and $CD$ by $E$, so that $|AB| = |BE|$. Denote the intersection of the tangents to $\mathcal{K}$ from $B$ and $D$ by $F$, so that $AB$ and $DF$ are parallel. Show that the points $A, C$ and $F$ are collinear.