The radius of the circle passing through the points \((5,7),(2,-2)\) and \((-2,0)\) is

(B)
Let \((\mathrm{h}, \mathrm{k})\) be the center of the circle which passes through \((5,7),(2,-2)\) and \((-2,0)\) \(\therefore(h-2)^{2}+(k+2)^{2}=(h+2)^{2}+k^{2}\)
\(\therefore-4 \mathrm{~h}+4+4 \mathrm{k}+4=4 \mathrm{~h}+4 \quad \Rightarrow 8 \mathrm{~h}-4 \mathrm{k}=4\) \(\Rightarrow 2 \mathrm{~h}-\mathrm{k}=1\)...(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 \(=3-(-2)=5\)