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Mexican equal segments

Source: Mexican Mathematical Olympiad 2005 OMM P6

July 31, 2018
geometryequal segments

Problem Statement

Let ABCABC be a triangle and ADAD be the angle bisector of <BAC<BAC, with DD on BCBC. Let EE be a point on segment BCBC such that BD=ECBD = EC. Through EE draw ll a parallel line to ADAD and let PP be a point in ll inside the triangle. Let GG be the point where BPBP intersects ACAC and FF be the point where CPCP intersects ABAB. Show BF=CGBF = CG.
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