MathNet 2019-part-03 — 184 problems (EN–VI) Question 111

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 the area of $XYZT$ is not less than twice the area of $ABCD$.