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(B) Let the center of the circle be $(h, k)$ and the radius be $r$.Since the circle touches the $x$-axis at $(1, 0)$,the distance from the center to t

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$10/3$

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(B) Let the center of the circle be $(h, k)$ and the radius be $r$.Since the circle touches the $x$-axis at $(1, 0)$,the distance from the center to the $x$-axis is equal to the radius,so $r = |k|$.The equation of the circle is $(x - h)^2 + (y - k)^2 = k^2$.Since the circle passes through $(1, 0)$,we have $(1 - h)^2 + (0 - k)^2 = k^2$,which simplifies to $(1 - h)^2 = 0$,so $h = 1$.The circle also passes through $(2, -3)$,so $(2 - 1)^2 + (-3 - k)^2 = k^2$.$1 + (9 + 6k + k^2) = k^2$.$10 + 6k = 0$.$6k = -10$,so $k = -5/3$.The radius $r = |k| = |-5/3| = 5/3$.The diameter of the circle is $2r = 2 	imes (5/3) = 10/3$.

The length of the diameter of a circle which touches the $x$-axis at the point $(1, 0)$ and passes through the point $(2, -3)$ is:

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