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ASU 355 All Soviet Union MO 1983 (DEF)<= (ADE)+(BDF) areas

Source:

July 28, 2019
geometrygeometric inequalityinequalitiesareas

Problem Statement

The point DD is the midpoint of the side [AB][AB] of the triangle ABCABC . The points EE and FF belong to [AC][AC] and [BC][BC] respectively. Prove that the area of triangle DEFDEF area does not exceed the sum of the areas of triangles ADEADE and BDFBDF.
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