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right-triangle problem

Source: China south east mathematical olympiad 2006 day1 problem 2

July 4, 2013
geometrygeometric transformationreflectiongeometry unsolved

Problem Statement

In △ABC\triangle ABC, ∠ABC=90∘\angle ABC=90^{\circ}. Points D,GD,G lie on side ACAC. Points E,FE, F lie on segment BDBD, such that AE⊥BDAE \perp BD and GF⊥BDGF \perp BD. Show that if BE=EFBE=EF, then ∠ABG=∠DFC\angle ABG=\angle DFC.
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