Question 12
In triangle $ABC$ point $P$ divides side $AB$ in ratio $\frac{AP}{PB} = \frac{1}{4}$. The perpendicular bisector of segment $PB$ intersects side $BC$ at point $Q$. If $\text{area}(PQC) = \frac{4}{25}\text{area}(ABC)$ and $AC = 7$, find $BC$.