On the side $AB$ of an isosceles triangle $AB$ ($AC=BC$) lie points $P$ and $Q$ such that $\angle PCQ \le \frac{1}{2} \angle ACB$. Prove that $PQ \le \frac{1}{2} AB$.
Problem
Source: Tuymaada Junior 2001 p6
Tags: geometry, geometric inequality, isosceles, Isosceles Triangle