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(C) The equation of the circle is $(x - 7)^2 + (y + 1)^2 = 25$. The center is $C(7, -1)$ and the radius $r = 5$.Let $O$ be the origin $(0, 0)$. The di

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$\frac{\pi}{2}$

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(C) The equation of the circle is $(x - 7)^2 + (y + 1)^2 = 25$. The center is $C(7, -1)$ and the radius $r = 5$.Let $O$ be the origin $(0, 0)$. The distance $d$ from the origin to the center $C$ is $d = \sqrt{(7 - 0)^2 + (-1 - 0)^2} = \sqrt{49 + 1} = \sqrt{50} = 5\sqrt{2}$.Let $	heta$ be the angle between the tangents. The angle between the line joining the origin to the center and one of the tangents is $\frac{	heta}{2}$.In the right-angled triangle formed by the origin,the point of tangency,and the center,we have $\sin(\frac{	heta}{2}) = \frac{r}{d} = \frac{5}{5\sqrt{2}} = \frac{1}{\sqrt{2}}$.Thus,$\frac{	heta}{2} = \frac{\pi}{4}$,which implies $	heta = \frac{\pi}{2}$.

The angle between the tangents drawn from the origin to the circle $(x - 7)^2 + (y + 1)^2 = 25$ is:

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