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Turkey Junior Olympiad 2007, Part II - P1

Source:

January 20, 2013
geometrytrapezoidrhombusratioangle bisectorperpendicular bisector

Problem Statement

Let ABCDABCD be a trapezoid such that AD∥BCAD\parallel BC and ∣AB∣=∣BC∣|AB|=|BC|. Let EE and FF be the midpoints of [BC][BC] and [AD][AD], respectively. If the internal angle bisector of △ABC\triangle ABC passes through FF, find ∣BD∣/∣EF∣|BD|/|EF|.
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