To prove or disprove, $d(p,X\setminus B_1)=d(p,B_2\setminus B_1)$, where $B_1\subset B_2$

Question

In a metric space $(X,d)$, if $B_1=B(x,r_1), B_2=B(x,r_2)$ are two open balls with $r_1<r_2$, and $p\in B_1$, then how to prove or disprove, $$d(p,X\setminus B_1)=d(p,B_2\setminus B_1)?$$

Here, for $A\subset X,$

$$d(x,A):=\inf_{a\in A}d(x,a) .$$