<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
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