Three cities/Symmetric/Rail connection/Exercise

The city ${}S=(0,0)$ shall be connected by rails with the two cities ${}T=(a,b)$ and ${}U=(a,-b)$ with ${}a\geq 0$, ${}b>0$. The rails shall run along the ${}x$-axis until it ramifies into the two directions. Determine the ramification point, with as few rails as possible.

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