BG-MO 2003 Problem 2

Let $H$ be an arbitrary point on the altitude $CP$ of the acute triangle $ABC$ . The lines $AH$ and $BH$ intersect $BC$ and $AC$ in $M$ and $N$ , respectively. [list] (a) Prove that $\angle NPC =\angle MPC$ . (b) Let $O$ be the common point of $MN$ and $CP$ . An arbitrary line through $O$ meets the sides of quadrilateral $CNHM$ in $D$ and $E$ . Prove that $\angle EPC =\angle DPC$ . [/list]