(B)
Let $(\mathrm{h}, \mathrm{k})$ be the center of the circle which passes through $(5,7),(2,-2)$ and $(-2,0)$ $\therefore(h-2)^{2}+(k+2)^{2}=(h+2)^{2}+k^{2}$
$\therefore-4 \mathrm{~h}+4+4 \mathrm{k}+4=4 \mathrm{~h}+4 \quad \Rightarrow 8 \mathrm{~h}-4 \mathrm{k}=4 \quad \Rightarrow 2 \mathrm{~h}-\mathrm{k}=1$...(1)
Also $(\mathrm{h}-5)^{2}+(\mathrm{k}-7)^{2}=(\mathrm{h}+2)^{2}+\mathrm{k}^{2}$
$\therefore-10 \mathrm{~h}+25-14 \mathrm{k}+49=4 \mathrm{~h}+4 \Rightarrow 14 \mathrm{~h}+14 \mathrm{k}=70 \Rightarrow \mathrm{h}+\mathrm{k}=5$...(2)
Solving $(1)$ and $(2)$, we get, $\mathrm{h}=2, \mathrm{k}=3 \Rightarrow$ centre $=(2,3)$
$\therefore$ Radius $=3-(-2)=5$