Coordinates of Point of Reference of Normal Neighborhood

Theorem
Let $\struct {M, g}$ be an $n$-dimensional Riemannian manifold.

Let $U_p$ be the normal neighborhood for $p \in M$.

Let $\struct {U_p, \tuple {x^i} }$ be any normal coordinate chart.

Then the coordinates of $p$ are $\tuple {0, \ldots, 0}$.