MathDB

2

Part of 1986 Swedish Mathematical Competition

Problems(1)

\sqrt{S_1} + \sqrt{S_2} <= \sqrt{S} areas in quadrilateral

Source: 1986 Swedish Mathematical Competition p2

3/28/2021
The diagonals ACAC and BDBD of a quadrilateral ABCDABCD intersect at OO. If S1S_1 and S2S_2 are the areas of triangles AOBAOB and CODCOD and S that of ABCDABCD, show that S1+S2≤S\sqrt{S_1} + \sqrt{S_2} \le \sqrt{S}. Prove that equality holds if and only if ABAB and CDCD are parallel.
geometryGeometric Inequalitiestriangle area