There is a triangle with side lengths \(a\), \(b\)
and \(c\). Does there exist a triangle
with side lengths \(|a-b|\), \(|b-c|\) and \(|c-a|\)? Does it depend on what \(a\), \(b\)
and \(c\) are?
Recall that a triangle can be formed with side lengths \(x\), \(y\)
and \(z\) if and only if all the
inequalities \(x+y>z\), \(y+z>x\) and \(z+x>y\) hold.