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Romania EGMO TST 2022 Day 1 P3

Source:

February 15, 2022
romaniaEGMOgeometryInequality

Problem Statement

Let ABCDABCD be a convex quadrilateral and let OO be the intersection of its diagonals. Let P,Q,R,P,Q,R, and SS be the projections of OO on AB,BC,CD,AB,BC,CD, and DADA respectively. Prove that 2(OP+OQ+OR+OS)≤AB+BC+CD+DA.2(OP+OQ+OR+OS)\leq AB+BC+CD+DA.
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