I want to proof $d(A.B)^2=d(A,C)^2+d(B,C)^2$ for
with $(\vec a-\vec c) \bullet (\vec b - \vec c)=0$. I applied the definitions of distance and got
$d(A,B)^2=d(A,C)^2+d(B,C)^2 \Leftrightarrow ||\vec b - \vec a||^2= || \vec c - \vec b||^2+||\vec c - \vec a||^2$ but now I don't know how to proceed.
If someone could help me out, it would be great.