Problem

Source: 2018 Iran MO 3rd Geometry 1

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Incircle of triangle $ABC$ is tangent to sides $BC,CA,AB$ at $D,E,F$,respectively.Points $P,Q$ are inside angle $BAC$ such that $FP=FB,FP||AC$ and $EQ=EC,EQ||AB$.Prove that $P,Q,D$ are collinear.