If two tangents inclined at an angle 60^{circ | vedclass

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(D) Let $P$ be an external point from which two tangents $PA$ and $PC$ are drawn to a circle with center $O$ and radius $OA = 3 \, cm$.The angle betwe

Vedclass · Accepted Answer

$3 \sqrt{3}$

Vedclass · Answer

(D) Let $P$ be an external point from which two tangents $PA$ and $PC$ are drawn to a circle with center $O$ and radius $OA = 3 \, cm$.The angle between the two tangents is $\angle APC = 60^{\circ}$.Join $OP$. $OP$ is the angle bisector of $\angle APC$.Therefore,$\angle APO = \angle CPO = \frac{60^{\circ}}{2} = 30^{\circ}$.Since the tangent at any point of a circle is perpendicular to the radius through the point of contact,$OA \perp AP$.In the right-angled triangle $	riangle OAP$,we have:$	an(\angle APO) = \frac{OA}{AP}$$	an 30^{\circ} = \frac{3}{AP}$$\frac{1}{\sqrt{3}} = \frac{3}{AP}$$AP = 3 \sqrt{3} \, cm$.Thus,the length of each tangent is $3 \sqrt{3} \, cm$.

If two tangents inclined at an angle $60^{\circ}$ are drawn to a circle of radius $3 \, cm$,then the length of each tangent is equal to (in $cm$):

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