<Qua-2025-752>, hint 

Let AB=BC=CD=DA=a, AE=t BE=a-t

PE/PD=BE/CD=(a-t)/a QF/QB=DF/BC=t/a ---> PE/PD+QF/BQ=(a-t)/a+t/a=1

b>.Suppose line PA cut line CD in Q', Q'C=x, DF=y

AE/EB=Q'D/DC  <--> t/(a-t)=x/a ---> x=at/(a-t)

FD/BC=Q'D/DC   <--->y/a=x/(a+x),  Hence y=t<---> DF=AE. Q=Q'

P,A,Q are collinear