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Ratios in length of a triangle

Source: Indonesian MO (INAMO) 2009, Day 1, Problem 3

August 8, 2009
ratiogeometrygeometry unsolved

Problem Statement

For every triangle ABC ABC, let D,E,F D,E,F be a point located on segment BC,CA,AB BC,CA,AB, respectively. Let P P be the intersection of AD AD and EF EF. Prove that: \frac{AB}{AF}\times DC\plus{}\frac{AC}{AE}\times DB\equal{}\frac{AD}{AP}\times BC
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