OBM 2001 Problem 3

$ABC$ is a triangle $E, F$ are points in $AB$ , such that $AE = EF = FB$

$D$ is a point at the line $BC$ such that $ED$ is perpendiculat to $BC$ $AD$ is perpendicular to $CF$ . The angle CFA is the triple of angle BDF. ( $3\angle BDF = \angle CFA$ )

Determine the ratio $\frac{DB}{DC}$ .

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