MathDB

G4

Part of JOM 2015 Shortlist

Problems(1)

Inequality with concurrent cevians

Source: Junior Olympiad of Malaysia Shortlist 2015 G4

7/17/2015
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 .
inequalities