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Inequality on area of quadrilaterals

Source: ToT 2003 SO-4

June 26, 2011
inequalitiesgeometrygeometry unsolved

Problem Statement

Each side of 1×11 \times 1 square is a hypothenuse of an exterior right triangle. Let A,B,C,DA, B, C, D be the vertices of the right angles and O1,O2,O3,O4O_1, O_2, O_3, O_4 be the centers of the incircles of these triangles. Prove that a)a) The area of quadrilateral ABCDABCD does not exceed 22; b)b) The area of quadrilateral O1O2O3O4O_1O_2O_3O_4 does not exceed 11.
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