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Cono Sur Olympiad 2005, Problem 4

Source:

August 19, 2014
geometryincentergeometric transformationreflectionsymmetryperpendicular bisectorgeometry proposed

Problem Statement

Let ABCABC be a isosceles triangle, with AB=ACAB=AC. A line rr that pass through the incenter II of ABCABC touches the sides ABAB and ACAC at the points DD and EE, respectively. Let FF and GG be points on BCBC such that BF=CEBF=CE and CG=BDCG=BD. Show that the angle ∠FIG\angle FIG is constant when we vary the line rr.
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