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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $cm$):

Similar Questions

$P$ is in the exterior of $\odot (O, 9)$. $A$ tangent from $P$ touches the circle at $T$. If $PT = 40$,then $OP = \ldots$

$A$ tangent line drawn from a point $A$ outside $\odot(P, 5)$ touches the circle at $B.$ If $PA = 13$,then $AB = \dots$

$\odot(P, 3)$ and $\odot(P, 5)$ are two concentric circles. Chord $\overline{AB}$ of $\odot(P, 5)$ touches $\odot(P, 3)$ at $M$. Find $AB$.

In the given figure,$AT$ is a tangent to the circle with center $O$ such that $OT = 4 \, cm$ and $\angle OTA = 30^{\circ}$. Then $AT$ is equal to (in $cm$):

In the figure,if $PQR$ is the tangent to a circle at $Q$ whose center is $O$,$AB$ is a chord parallel to $PR$,and $\angle BQR = 70^{\circ}$,then $\angle AQB$ is equal to: (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module