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area inequality (XYZ) >= (AYZ), (BZX), (CXY)

Source: 1981 Swedish Mathematical Competition p5

March 28, 2021
geometryGeometric Inequalitiesareas

Problem Statement

ABCABC is a triangle. XX, YY, ZZ lie on BCBC, CACA, ABAB respectively. Show that area XYZXYZ cannot be smaller than each of area AYZAYZ, area BZXBZX, area CXYCXY.
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