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1964 AMC 12 Question 32

AMC12 · 1964 AMC 12

Question 32

If $\dfrac{a+b}{b+c}=\dfrac{c+d}{d+a},$ then:
  1. $a$ must equal $c$
  2. $a+b+c+d$ must equal zero
  3. either $a=c$ or $a+b+c+d=0,$ or both
  4. $a+b+c+d\ne0$ if $a=c$
  5. $a(b+c+d)=c(a+b+d)$