Distance between a point and the boundary of a subset D

Question

I have to implement an article and i end up struggling on this:

Given the subset $D= \{ y , |y -x| < a \}$ in $\mathbb{R}^{d}$ , i have to determine $d(X_{t},\partial D)$ , i know the value of a , i know $x = X_{0}$ , the process is at value in $\mathbb{R}^{d}$ How do i determine this distance in dimension $d > 1$. Is it possible or not ?

Answer 1

The set $\partial D$ is the sphere of radius $a$ centered at $x$, so $d(X_t, {\partial D})=|\|X_t-x\|-a|$.