The angle between the tangents drawn from the | vedclass

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Question

(C) The circle is $(x - 7)^2 + (y + 1)^2 = 5^2$. The center is $C(7, -1)$ and the radius $r = 5$.Let the distance from the origin $O(0, 0)$ to the cen

Vedclass · Accepted Answer

$\pi /2$

Vedclass · Answer

(C) The circle is $(x - 7)^2 + (y + 1)^2 = 5^2$. The center is $C(7, -1)$ and the radius $r = 5$.Let the distance from the origin $O(0, 0)$ to the center $C(7, -1)$ be $d$.$d = \sqrt{7^2 + (-1)^2} = \sqrt{49 + 1} = \sqrt{50} = 5\sqrt{2}$.Let $	heta$ be the angle between the tangents. Then $\sin(	heta / 2) = \frac{r}{d} = \frac{5}{5\sqrt{2}} = \frac{1}{\sqrt{2}}$.Thus,$	heta / 2 = 45^\circ = \pi / 4$.Therefore,$	heta = 2 	imes (\pi / 4) = \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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