MathDB
(AOB)+ (COD) <= 2(AOD)+ 2(BOC), with areas in convex ABCD

Source: Sharygin 2013 Final 9.3

August 19, 2018
geometryInequalityareas

Problem Statement

Each sidelength of a convex quadrilateral ABCDABCD is not less than 11 and not greater than 22. The diagonals of this quadrilateral meet at point OO. Prove that SAOB+SCOD≤2(SAOD+SBOC)S_{AOB}+ S_{COD} \le 2(S_{AOD}+ S_{BOC}).
Back to ProblemsView on AoPS