KöMaL 2008 B4096

The points of tangency of the inscribed circle on the sides of a triangle ABC are $E$, $F$and $G$. The distances of an arbitrary point $P$ of the inscribed circle from the sides are $a$, $b$ and $c$, and its distances from the lines $FG$, $EG$ and $EF$ are $e$, $f$and $g$. Prove that abc = efg .