Let $ABC$ be a triangle with $\angle B \ge 2\angle C$. Denote by $D$ the foot of the altitude from $A$ and by $M$ be the midpoint of $BC$. Prove that $DM \ge \frac{AB}{2}$.
Source: 2010 Saudi Arabia IMO TST II p1
Tags: geometric inequality, geometry
Let $ABC$ be a triangle with $\angle B \ge 2\angle C$. Denote by $D$ the foot of the altitude from $A$ and by $M$ be the midpoint of $BC$. Prove that $DM \ge \frac{AB}{2}$.