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The geometric median of a domain is the point that minimises the averagedistance from itself to the points of the domain. We will give a gradientsystem of equations that defines the geometric median of a triangular domainand will prove a simple geometric property of the median. This property statesthat all three average distances from the median to the sides of the triangleare equal. Further we generalise these results to other types of domains and toother types of median like points.

On the geometric median of triangular domains and other median type points