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Iran TST

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

April 10, 2019
geometryparallelogram

Problem Statement

Point PP lies inside of parallelogram ABCDABCD. Perpendicular lines to PA,PB,PCPA,PB,PC and PDPD through A,B,CA,B,C and DD construct convex quadrilateral XYZTXYZT. Prove that SXYZT≥2SABCDS_{XYZT}\geq 2S_{ABCD}.
Proposed by Siamak Ahmadpour
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