Question 93
Let $ABC$ be an acute-angled triangle such that $|AB| \gt |AC|$, and let $D$, $E$ and $F$ be the feet of its altitudes from the vertices $A$, $B$ and $C$, respectively. The lines $EF$ and $BC$ intersect at the point $P$. The line passing through $D$ parallel to $EF$ intersects the lines $AC$ and $AB$ at the points $Q$ and $R$, respectively.
If $N$ is a point on the segment $\overline{BC}$ such that $\angle NQP + \angle NRP \lt 180^\circ$, prove that $|BN| \gt |CN|$.
(South Africa 2010)
If $N$ is a point on the segment $\overline{BC}$ such that $\angle NQP + \angle NRP \lt 180^\circ$, prove that $|BN| \gt |CN|$.
(South Africa 2010)