I want to conclude that $B_r(x_0)$ is convex from the fact that $B_1(0)$ is convex. So I was trying to use the answer provided here Proving that closed (and open) balls are convex
But the thing is that I don't know how to conclude, I think that they may be need that $B_1(0)$ is convex to get the result. Can someone help me to get this result please?
Thanks a lot in advance.