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inequality with areas

Source: Tuymaada 2013, Day 2, Problem 8 Juniors

July 26, 2013
inequalitiesgeometryperimeteranalytic geometrytrigonometrygeometry proposed

Problem Statement

The point A1A_1 on the perimeter of a convex quadrilateral ABCDABCD is such that the line AA1AA_1 divides the quadrilateral into two parts of equal area. The points B1B_1, C1C_1, D1D_1 are defined similarly. Prove that the area of the quadrilateral A1B1C1D1A_1B_1C_1D_1 is greater than a quarter of the area of ABCDABCD.
L. Emelyanov
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