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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 $PO=11$.

 Sep 2, 2022
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I solve this before.  The possible length of TP are 3 and 4, and the possible lengths TO are 6, 7, and 8.

 Sep 2, 2022

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