Problem

Source: Bulgarian MO 2003: P2

Tags: geometry unsolved, geometry



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. (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 $\angle EPC =\angle DPC$.