Simplifying $XX^T$ under some assumption

Question

Let a matrix $D$ where $$D_{i,j} = d(i, j) = \|x_i -x_j\|$$ and $x_i, x_j \in \mathbb{R}^2$ representing a location.

I already showed that for $X\in \mathbb{R}^{312\times 2}$:

$$(XX^T)_{i,j} = \frac{\|x_i\|^2 + \|x_j\|^2 - d(i, j)^2}{2}$$

Now I am asked to simplify $XX^T$ under the assumption that: $\sum_i x_i = (0, 0)$

I'm struggling with that and be glad for help.

Thanks!