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UKMT Senior Kangaroo, 2015

Algebra Difficulty 3.0 AMC 10/12 Prove it United Kingdom

Numbers $a$ , $b$ and $c$ are such that $\dfrac{a}{b+c} = \dfrac{b}{c+a} = \dfrac{c}{a+b} = k$ . How many possible values of $k$ are there?

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