Consider the circles x^2 + (y - 1)^2 = 9 and | vedclass

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(B) The equations of the circles are $x^2 + (y - 1)^2 = 3^2$ and $(x - 1)^2 + y^2 = 5^2$. The centers are $C_1 = (0, 1)$ and $C_2 = (1, 0)$. The radii

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One circle lies entirely inside the other.

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(B) The equations of the circles are $x^2 + (y - 1)^2 = 3^2$ and $(x - 1)^2 + y^2 = 5^2$. The centers are $C_1 = (0, 1)$ and $C_2 = (1, 0)$. The radii are $r_1 = 3$ and $r_2 = 5$. The distance between the centers is $d = \sqrt{(1 - 0)^2 + (0 - 1)^2} = \sqrt{1^2 + (-1)^2} = \sqrt{2} \approx 1.414$. We check the condition for one circle lying inside another: $|r_2 - r_1| = |5 - 3| = 2$. Since $d < |r_2 - r_1|$ (because $\sqrt{2} < 2$),one circle lies entirely inside the other.

Consider the circles $x^2 + (y - 1)^2 = 9$ and $(x - 1)^2 + y^2 = 25$. Which of the following is true?

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