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SMO 2015 Junior Round 1 Question 4

SMO · SMO 2015 Junior Round 1

Question 4

If $a,b$ and $c$ are positive real numbers such that $$\frac a{a+b}=\frac{a+b}{a+b+c}=\frac c{b+c},$$ then $\dfrac ab$ equals
  1. $\frac{\sqrt{3}-1}{2}$
  2. 1
  3. $\sqrt{2}$
  4. $\frac{1+\sqrt{5}}{2}$
  5. None of the above