## Τρίτη, 10 Οκτωβρίου 2017

### 2008 JBMO Shortlist G4

Let $ABC$ be a triangle, ($BC < AB$). The line $l$ passing trough the vertices $C$ and orthogonal to the angle bisector $BE$ of $\angle B$, meets $BE$ and the median $BD$ of the side $AC$ at points $F$ and $G$, respectively. Prove that segment $DF$ bisects the segment $EG$.

posted in aops here