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(D) The center of the circle is the intersection point of its diameters $x + y = 6$ and $x + 2y = 4$.Subtracting the first equation from the second: $

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$\sqrt{20}$

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(D) The center of the circle is the intersection point of its diameters $x + y = 6$ and $x + 2y = 4$.Subtracting the first equation from the second: $(x + 2y) - (x + y) = 4 - 6 \implies y = -2$.Substituting $y = -2$ into $x + y = 6$,we get $x - 2 = 6 \implies x = 8$.Thus,the center of the circle is $(8, -2)$.The circle passes through the point $(6, 2)$.The radius $r$ is the distance between the center $(8, -2)$ and the point $(6, 2)$.$r = \sqrt{(6 - 8)^2 + (2 - (-2))^2} = \sqrt{(-2)^2 + (4)^2} = \sqrt{4 + 16} = \sqrt{20}$.

The radius of the circle passing through the point $(6, 2)$ and whose two diameters are $x + y = 6$ and $x + 2y = 4$ is

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