Grade 11 2007 Problem 2

U trokutu $ABC$ s kutom $\measuredangle BAC = 120^{\circ}$ simetrale kutova $\measuredangle BAC$, $\measuredangle ABC$ i $\measuredangle BCA$ sijeku nasuprotne stranice u točkama $D$, $E$ i $F$ redom. Dokažite da kružnica s promjerom $\overline{EF}$ prolazi kroz $D$.