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CAT 2012 | Question: 13

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If $a= \dfrac{x}{y+z},b= \dfrac{y}{z+y},c= \dfrac{z}{x+y}$, then which of the following statements is/are true?

  1. $\dfrac{b+c-1}{yz}+\dfrac{a+c-1}{xz}+\dfrac{a+b-1}{yx}=1 \\$
  2. $\dfrac{x^{2}}{a(1-bc)}= \dfrac{y^{2}}{b(1-ca)}= \dfrac{z^{2}}{c(1-ab)} \\$
  3. $(a+b)c+(b+c)a+(a+c)b= \dfrac{2(x+y+z)(xy+xz+yz)-6xyz}{(x+y)(y+z)(z+x)}$
  1. I and II
  2. I and III
  3. II and III
  4. None of these
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