CN-LEAGUE 2001 Problem 1

Let $O,H$ be the circumcenter and orthocenter of $\triangle ABC,$ respectively. Line $AH$ and $BC$ intersect at $D,$ Line $BH$ and $AC$ intersect at $E,$ Line $CH$ and $AB$ intersect at $F,$ Line $AB$ and $ED$ intersect at $M,$ $AC$ and $FD$ intersect at $N.$ Prove that $(1)OB\perp DF,OC\perp DE;$ $(2)OH\perp MN.$