AMO 2021 – Junior College (Grades 11–12) Question 22

Quadrilateral $ABCD$ is cyclic. Diagonal $BD$ bisects $\angle ABC=\pi/3$. Point $E$ is on the extension of $BC$ beyond $C$, with $CE=AB=4$ inches. Also $BC=6$ inches and $DF\perp BC$ at $F$. Find $CF$ in inches.