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(B) Let the center of the circle be $(h, k)$ and the radius be $r$. The circle passes through $A(5,7)$,$B(2,-2)$,and $C(-2,0)$.Since the distance from

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$5$

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(B) Let the center of the circle be $(h, k)$ and the radius be $r$. The circle passes through $A(5,7)$,$B(2,-2)$,and $C(-2,0)$.Since the distance from the center to each point is equal to $r$,we have $r^2 = (h-2)^2 + (k+2)^2 = (h+2)^2 + k^2$.Expanding this: $h^2 - 4h + 4 + k^2 + 4k + 4 = h^2 + 4h + 4 + k^2$.Simplifying,we get $-8h + 4k = -4$,or $2h - k = 1$ $(1)$.Also,$(h-5)^2 + (k-7)^2 = (h+2)^2 + k^2$.Expanding this: $h^2 - 10h + 25 + k^2 - 14k + 49 = h^2 + 4h + 4 + k^2$.Simplifying,we get $-14h - 14k = -70$,or $h + k = 5$ $(2)$.Adding $(1)$ and $(2)$,we get $3h = 6$,so $h = 2$. Substituting $h=2$ into $(2)$,we get $k = 3$.The center is $(2, 3)$.The radius $r$ is the distance from $(2, 3)$ to $(-2, 0)$:$r = \sqrt{(2 - (-2))^2 + (3 - 0)^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$ units.

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

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