A geometry problem by Paola Ramírez

Geometry Level 4

In a \(\triangle ABC\), the bisector of \(\angle B\) cuts \(AC\) on \(D\) and intersects \(\triangle ABC\) circumcircle on \(E\). \(\triangle DAE\) circumcircle cuts again \(AB\) on \(F\).

Find \(\dfrac{\text{Area} \triangle DBC}{\text{Area} \triangle DBF}\).

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