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(C) The radius $r$ of the circle is the perpendicular distance from the center $(0, 0)$ to the line $5x + 12y - 1 = 0$.$r = \frac{|5(0) + 12(0) - 1|}{

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$169 (x^2 + y^2) = 1$

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(C) The radius $r$ of the circle is the perpendicular distance from the center $(0, 0)$ to the line $5x + 12y - 1 = 0$.$r = \frac{|5(0) + 12(0) - 1|}{\sqrt{5^2 + 12^2}} = \frac{|-1|}{\sqrt{25 + 144}} = \frac{1}{\sqrt{169}} = \frac{1}{13}$.The equation of a circle with center $(0, 0)$ and radius $r$ is $x^2 + y^2 = r^2$.Substituting $r = \frac{1}{13}$,we get $x^2 + y^2 = (\frac{1}{13})^2 = \frac{1}{169}$.Multiplying both sides by $169$,we get $169(x^2 + y^2) = 1$.

If a circle with center $(0, 0)$ touches the line $5x + 12y = 1$,then its equation is:

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