MathDB
2S <=OA OC+ OBxOB for tangential ABCD

Source: VI Soros Olympiad 1990-00 R2 11.3 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 28, 2024
geometrygeometric inequalitytangential

Problem Statement

A convex quadrilateral ABCDABCD has an inscribed circle touching its sides ABAB, BCBC, CDCD, DADA at the points MM,NN,PP,KK, respectively. Let OO be the center of the inscribed circle, the area of the quadrilateral MNPKMNPK is equal to 88. Prove the inequality 2S≤OA⋅OC+OB⋅OD.2S \le OA \cdot OC+ OB \cdot OD.
Back to ProblemsView on AoPS