Question 49
Let $ABC$ be an acute triangle, $CP$ its altitude to $AB$, and $H$ any point on $CP$. Lines $AH,BH$ meet $BC,AC$ at $M,N$.
(1) Prove $\angle NPC=\angle MPC$.
(2) Let $O=MN\cap CP$. An arbitrary line through $O$ meets the sides of quadrilateral $CNHM$ at $D,E$. Prove $\angle EPC=\angle DPC$.
(1) Prove $\angle NPC=\angle MPC$.
(2) Let $O=MN\cap CP$. An arbitrary line through $O$ meets the sides of quadrilateral $CNHM$ at $D,E$. Prove $\angle EPC=\angle DPC$.