Let $\Omega\subset \mathbb R^n$ be a compact domain of dimension $n$. Define the *geometric median* on $\Omega$ as the point $m_{\Omega}\in \mathbb R^n$ such that the integral $\int_{\Omega}|x-m_{\Omega}|dx$ attains its minimum.

**Question** Suppose that the domain $\Omega$ is a triangle $\Delta$ in $\mathbb R^2$. Is there a closed formula for the geometric median of $\Delta$?

**Disclaimer.** The name *geometric median* is taken from the Wikipedia article
https://en.wikipedia.org/wiki/Geometric_median . There is huge amount of articles, in particular in statistics, probability, location theory, ect, that use this notion. It is clear as well that this notion has a lot of different names (some of which are given in the Wikipedia article). This notion is mainly applied to the case when $\Omega$ is a finite set. However, after an extensive search on Google, MathSciNet, Google Scholar, etc. I was not able to find any reasonable source treating the above question.

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