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t (a, b, c)= min{b/a,c/b} where a <= b <= c , sidelengths

Source: Germany Federal - Bundeswettbewerb Mathematik 2010, round 2, p1

April 14, 2020

inequalitiesalgebrasidelengthsgeometric inequality

Problem Statement

Let

a, b, c

be the side lengths of an non-degenerate triangle with

a \le b \le c

. With

t (a, b, c)

denote the minimum of the quotients

\frac{b}{a}

and

\frac{c}{b}

. Find all values that

t (a, b, c)

can take.