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IMO LongList 1967, Bulgaria 4

Source: IMO LongList 1967, Bulgaria 4

November 14, 2004

geometrygeometric inequalityconstructionmedianTriangleIMO ShortlistIMO Longlist

Problem Statement

Suppose medians

m_a

and

m_b

of a triangle are orthogonal. Prove that: a.) Using medians of that triangle it is possible to construct a rectangular triangle. b.) The following inequality:

5(a^2+b^2-c^2) \geq 8ab,

is valid, where

a,b

and

c

are side length of the given triangle.

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