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$a,b$ and $c$ are the lengths of the triangle $\text{ABC}$ and $d,e$ and $f$ are the lengths of the sides of the triangle $\text{DEF}$. If the following equations hold true:

  • $a(a+b+c)=d^2$
  • $b(a+b+c)=e^2$
  • $c(a+b+c)=f^2$

then which of the following is always true of triangle $\text{DEF}?$

  1. It is an acute-angled triangle
  2. It is an right-angled triangle
  3. It is an obtuse-angled triangle
  4. None of the above
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