This is an impossible question.
Suppose that $R'$ is a point such that $R-R'-S$ and a point $T'$ such that $T-T'-S~\&~\overline{RT}\|\overline{R'T'}$
Observe that the new triangle $\Delta SR'T'$ does not change the given in the problem in any way.
How can anything be proven if that is the case?