There are four points $T,I,P,$ and $O$ in the plane. Suppose $\triangle TIP$ and $\triangle TOP$ are isosceles triangles. Also suppose that $TI=5,$ $PI=7,$ and $PO=11$.

I solve this before. The possible length of TP are 3 and 4, and the possible lengths TO are 6, 7, and 8.