MathDB
Inequality with concurrent cevians

Source: Junior Olympiad of Malaysia Shortlist 2015 G4

July 17, 2015
inequalities

Problem Statement

Let ABC ABC be a triangle and let AD,BE,CF AD, BE, CF be cevians of the triangle which are concurrent at G G . Prove that if CF⋅BE≥AF⋅EC+AE⋅BF+BC⋅FE CF \cdot BE \ge AF \cdot EC + AE \cdot BF + BC \cdot FE then AG≤GD AG \le GD .
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