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RMT 2015 Geometry #6

Source:

October 28, 2022
geometry

Problem Statement

In a triangle ABCABC, let DD and EE trisect BCBC, so BD=DE=ECBD = DE = EC. Let FF be the point on ABAB such that AFFB=2\frac{AF}{F B}= 2, and GG on ACAC such that AGGC=12\frac{AG}{GC} =\frac12 . Let PP be the intersection of DGDG and EFEF, and extend APAP to intersect BCBC at a point XX. Find BXXC\frac{BX}{XC}
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