MathNet 2016-part-07 — 182 problems (EN–VI) Question 90

Let $ABCD$ be a rectangle, and let $E$ and $F$ be points on segment $AB$ such that $AE = EF = FB$. If $CE$ intersects the line $AD$ at $P$, and $PF$ intersects $BC$ at $Q$, determine the ratio of $BQ$ to $CQ$.