MathDB

16

Part of 2016 Baltic Way

Problems(1)

Parallel lines

Source: Baltic Way 2016, Problem 16

11/5/2016
In triangle ABC,ABC, the points DD and EE are the intersections of the angular bisectors from CC and BB with the sides ABAB and AC,AC, respectively. Points FF and GG on the extensions of ABAB and ACAC beyond BB and C,C, respectively, satisfy BF=CG=BC.BF = CG = BC. Prove that FG∥DE.F G \parallel DE.
geometry