In $\triangle ABC$, we have three edges with lengths $BC=a, \, CA=b \, AB=c$, and $c<b<a<2c$. $P$ and $Q$ are two points of the edges of $\triangle ABC$, and the straight line $PQ$ divides $\triangle ABC$ into two parts with the same area. Find the minimum value of the length of the line segment $PQ$.