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Bundeswettbewerb Mathematik 1978 Problem 2.1

Source: Bundeswettbewerb Mathematik 1978 Round 2

October 12, 2022
inequalitiesTrianglealgebra

Problem Statement

Let a,b,ca, b, c be sides of a triangle. Prove that 13≤a2+b2+c2(a+b+c)2<12\frac{1}{3} \leq \frac{a^2 +b^2 +c^2 }{(a+b+c)^2 } < \frac{1}{2} and show that 12\frac{1}{2} cannot be replaced with a smaller number.
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