There is a triangle with side lengths \(a\), \(b\)
and \(c\). Can you form a triangle with
side lengths \(\frac{a}{b}\), \(\frac{b}{c}\) and \(\frac{c}{a}\)? Does it depend on what \(a\), \(b\)
and \(c\) are? Give a proof if it is
always possible or never possible. Otherwise, construct examples to show
the dependence on \(a\), \(b\) and \(c\).
Recall that a triangle can be drawn with side lengths \(x\), \(y\)
and \(z\) if and only if \(x+y>z\), \(y+z>x\) and \(z+x>y\).