MathNet 2001 — Part 01 Question 122

In triangle $ABC$, $\angle B = 2\angle C$. Let $P$ and $Q$ be points on the perpendicular bisector of segment $BC$ such that rays $AP$ and $AQ$ trisect $\angle A$. Prove that $PQ \lt AB$ if and only if $\angle B$ is obtuse.