Question 34
Let $ABC$ be an acute triangle. Let $H$ denote its orthocenter and $D$, $E$ and $F$ the feet of its altitudes from $A$, $B$ and $C$, respectively. Let the common point of $DF$ and the altitude through $B$ be $P$. The line perpendicular to $BC$ through $P$ intersects $AB$ in $Q$. Furthermore, $EQ$ intersects the altitude through $A$ in $N$.
Prove that $N$ is the mid-point of $AH$.
(Karl Czakler)
Figure 3: Problem 13
Prove that $N$ is the mid-point of $AH$.
(Karl Czakler)
Figure 3: Problem 13