Prove that the two balls $B(x,0.8)$ and $B(y,0.8)$ which are both contained in $B(0,1)$ intersect

Question

Prove that the two open balls $B(x,0.8)$ and $B(y,0.8)$ which are both contained in $B(0,1)$ intersect.

We are looking at the metric space $(R^n,d_{1,2 or \infty})$

This makes sense thinking of the example in $R^3$ with metric $d_2$, but I'm having trouble generalizing. Should I be going about this in separate cases for each metric? Is the triangle inequality helpful?

Really appreciate any help!