Question 102
Suppose that the convex quadrilateral $ABCD$ satisfies $AB = BC$, $AD = DC$. $E$ is a point on $AB$, and $F$ on $AD$, such that $B$, $E$, $F$, $D$ are concyclic. Draw $\triangle DPE$ directly similar to $\triangle ADC$, and $\triangle BQF$ directly similar to $\triangle ABC$. Prove that $A$, $P$, $Q$ are collinear. (Posed by Ye Zhonghao)
