Let $ABC$ be a triangle such that $AB < BC$. Plot the height $BH$ with $H$ in $AC$. Let I be the incenter of triangle $ABC$ and $M$ the midpoint of $AC$. If line $MI$ intersects $BH$ at point $N$, prove that $BN < IM$.
Source: 2009 Peru Iberoamerican TST problem 4
Tags: geometry
Let $ABC$ be a triangle such that $AB < BC$. Plot the height $BH$ with $H$ in $AC$. Let I be the incenter of triangle $ABC$ and $M$ the midpoint of $AC$. If line $MI$ intersects $BH$ at point $N$, prove that $BN < IM$.