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

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

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Solution:

Let $O P$ and $O Q$ are the tangents drawn from the origin to the given circle (draw a figure).
Now, center $C \equiv(7,1)$ and the radius $C P=5$.
Also $O C=\sqrt{49+1}=5 \sqrt{2}$.
If ' $2 A$ ' is the angle between the $2$ tangents then
$\sin A=\frac{C P}{O C}=\frac{5}{5 \sqrt{2}}=\frac{1}{\sqrt{2}}$.
$\therefore A=\pi / 4$
$ \therefore 2 A=\pi / 2$

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