Calculating the point located at a furthest distance from input points

Let's say we have a cluster of 10 points that fall inside a coordinate system. Inside this cluster, we need to find another point which has such a location that has to be as far as possible from any other point. In other words, it satisfies a furthest distance from any other point.

How do we find out the coordinates of this point?

Re: Calculating the point located at a furthest distance from input points

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**Ardit700** Let's say we have a cluster of 10 points that fall inside a coordinate system. Inside this cluster, we need to find another point which has such a location that has to be as far as possible from any other point. In other words, it satisfies a furthest distance from any other point. How do we find out the coordinates of this point?

This may not be what you are asking. But surely you need to already know the coordinates of each point. So this comes down to finding the point at the greatest distance from the rest of the set. For each $\displaystyle n$ let $\displaystyle \delta_n=\min\{d(x_n,x_m):n\ne m\}$, that is using the ordinary metric $\displaystyle d$. Now let $\displaystyle M=\max\{\delta_n\}$ so $\displaystyle \exists(j)$ and $\displaystyle M=\delta_j$. Thus $\displaystyle x_j$ is your point.