**Problem of the Week**

Problem E

Terry’s Triangles

Terry is drawing isosceles triangles with side lengths \(a\), \(b\), and \(c\) such that \[\begin{aligned}
a&=y-x\\
b&=x+z\\
c&=y-z\end{aligned}\] where \(x\), \(y\), and \(z\) are positive integers and \(x+y+z<10\).

Find all the possible triples \((a,b,c)\) that satisfy this.