KöMaL 2005 C819

A fly is sitting at the centre $K$ of a regular hexagon ABCDEF , there is another fly at vertex $B$ and a spider sitting at vertex $A$. The flies start clawling from $B$ towards $C$ and from $K$ towards $E$ simultaneously at the same speed. (The spider stays in placed.) Show that the three of them form a regular triangle at every time instant.