KöMaL 2012 B4460

Regular triangles ABD , BCE and CAF are drawn over the sides of a triangle ABC , on the outside. Let $G$ and $H$ denote the midpoints of the line segments $BD$ and $BE$, respectively, and let the midpoint of triangle CAF be $I$. Prove that the lines $AH$, $CG$ and $BI$ are concurrent.