Suppose I have any three numbers $a,b,$ and $c$. I'm wondering if it's true in general that
$$||a - c| - |b - c || = |a - b|$$
I've been testing this out with numbers and thinking about it in terms of length of lines and it seems to hold true. But I haven't been able to prove it using properties of absolute value.
Edit: Assuming $a$,$b$, and $c$ are all constant