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2

Part of 1969 Czech and Slovak Olympiad III A

Problems(1)

Bounded are of a convex quadrilateral

Source: Czech and Slovak Olympiad 1969, National Round, Problem 2

7/3/2024
Five different points O,A,B,C,DO,A,B,C,D are given in plane such that OA≤OB≤OC≤OD.OA\le OB\le OC\le OD. Show that for area PP of any convex quadrilateral with vertices A,B,C,DA,B,C,D (not necessarily in this order) the inequality P≤12(OA+OD)(OB+OC)P\le \frac12(OA+OD)(OB+OC) holds and determine when equality occurs.
geometryGeometric Inequalitiesgeometrical inequalitiesconvexquadrilateralarea