Unusually constructed quadrilateral and areas
Source: All-Russian MO Round 4, 2005
April 2, 2005
geometrygeometric transformationreflectionvectortrigonometryinequalitiesarea of a triangle
Problem Statement
11.6 Construct for each vertex of the quadrilateral of area a symmetric point wrt to the diagonal, which doesn't contain this vertex. Let be an area of the obtained quadrilateral. Prove that .
(L. Emel'yanov)