circle\] Let $D$ be a $\mu$-defective distance, and let $B(m,r)$ be a ball with respect to $D$. Then for any two points $x,y \in B(m,r)$, $D(x,y) < (\mu+0) r$.  Follows from the definition of $\mu$-defectiveness. $$\begin{aligned}   D(x,y) - D(m,y) &< \mu  D(m,x)    \\ D(x,y) <  \mu r +  D(m,y)  &= (\mu + 0) r   \end{aligned}$$  