sqrt([AKON]) + sqrt([CLOM]) <= sqrt([ABCD])
Source: IMO Shortlist 1995, G7
December 30, 2005
geometryinequalitiesIMO Shortlistsimilar trianglesgeometric inequalityquadrilateral
Problem Statement
Let ABCD be a convex quadrilateral and O a point inside it. Let the parallels to the lines BC, AB, DA, CD through the point O meet the sides AB, BC, CD, DA of the quadrilateral ABCD at the points E, F, G, H, respectively. Then, prove that \sqrt {\left|AHOE\right|} \plus{} \sqrt {\left|CFOG\right|}\leq\sqrt {\left|ABCD\right|}, where is an abbreviation for the non-directed area of an arbitrary polygon .