  The geometric median of a domain is the point that minimises the average
distance from itself to the points of the domain. We will give a gradient
system of equations that defines the geometric median of a triangular domain
and will prove a simple geometric property of the median. This property states
that all three average distances from the median to the sides of the triangle
are equal. Further we generalise these results to other types of domains and to
other types of median like points.
