Suppose a set of $n$ high-dimensional points is given. It is known that the sum of all pair-wise squared Euclidean distances is proportional to sum of squared distances of all points to the centroid.
However, given a specific point $a$, in what relation is the sum of squared Euclidean distances from $a$ to all other points, and the square Euclidean distance of $a$ from the centroid of all points (including $a$).