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TOT 202 1988 Autumn S6 S <=AM x CM + BM x DM, rectangle

Source:

March 7, 2021
geometryrectanglegeometric inequality

Problem Statement

MM is an interior point of a rectangle ABCDABCD and SS is its area. Prove that SAMCM+BMDMS \le AM \cdot CM + BM \cdot DM.
(I.J . Goldsheyd)