Question 8
A point $E$ is chosen on the side $AB$ of a rectangle $ABCD$ ($E \neq A, E \neq B$). The line segments $BD$ and $CE$ intersect at point $F$. Among the triangles $ADE$, $DEF$, $DCF$, $BCF$ and $BEF$, there are exactly two pairs of triangles with equal area (the order of components in a pair is not taken into account). Find the ratio of the lengths of the line segments $EB$ and $AB$.