MathDB

355

Part of 1983 All Soviet Union Mathematical Olympiad

Problems(1)

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

Source:

7/28/2019
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.
geometrygeometric inequalityinequalitiesareas