For a triangle $\Delta$, let (P) denote the problem of the existence ofpoints in the plane of $\Delta$, that are at rational distance to the 3vertices of $\Delta$. Answer to (P) is known to be positive in the followingsituation: $\Delta$ has one rational side and the square of all sides arerational. Further, the set of solution-points is dense in the plane of$\Delta$. See [3] The reader can convince himself that the rationality of oneside is a reasonable minimum condition to set out, otherwise problem (P) wouldstay somewhat hazy and scattered. Now, even with the assumption of one rationalside, problem (P) stays hard. In this note, we restrict our attention toisosceles triangles, and provide a \textit{complete description} of suchtriangles for which (P) has a positive answer.
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