Question 35
$\mathrm{M}$ is the midpoint of the median $\mathrm{AD}$ of the triangle $\mathrm{ABC}$. The ray $\mathrm{BM}$ meets $\mathrm{AC}$ at $N$. Show that $\mathrm{AB}$ is tangent to the circumcircle of $\mathrm{NBC}$ iff $\mathrm{BM} / \mathrm{BN}=(\mathrm{BC} / \mathrm{BN})^{2}$.