Problem

Source: Iranian TST 2019, first exam, day1, problem 3

Tags: geometry, parallelogram



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