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SMO 2010 Senior Round 1 Question 2

SMO · SMO 2010 Senior Round 1

Question 2

If $a,b,c,d$ are real numbers such that

$$\frac{b+c+d}{a}=\frac{a+c+d}{b}=\frac{a+b+d}{c}=\frac{a+b+c}{d}=r,$$

find the value of $r$.
  1. $3$
  2. $1$
  3. $-1$
  4. $3$ or $1$
  5. $3$ or $-1$