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Turkey TST 2008 Q5

Source:

April 2, 2008
trigonometrygeometryangle bisectorgeometry unsolved

Problem Statement

D D is a point on the edge BC BC of triangle ABC ABC such that AD\equal{}\frac{BD^2}{AB\plus{}AD}\equal{}\frac{CD^2}{AC\plus{}AD}. E E is a point such that D D is on [AE] [AE] and CD\equal{}\frac{DE^2}{CD\plus{}CE}. Prove that AE\equal{}AB\plus{}AC.
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