IR-TST 2019 Problem 3

Point $P$ lies inside of parallelogram $ABCD$ . Perpendicular lines to $PA,PB,PC$ and $PD$ through $A,B,C$ and $D$ construct convex quadrilateral $XYZT$ . Prove that $S_{XYZT}\geq 2S_{ABCD}$ .

Proposed by Siamak Ahmadpour