In the given figure,AT is a tangent to the ci | vedclass

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

Question

(A) In $	riangle OAT$,we know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.Therefore,$\angle

Vedclass · Accepted Answer

$2 \sqrt{3}$

Vedclass · Answer

(A) In $	riangle OAT$,we know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.Therefore,$\angle OAT = 90^{\circ}$.In the right-angled triangle $	riangle OAT$,we have:$\cos(\angle OTA) = \frac{	ext{Adjacent side}}{	ext{Hypotenuse}} = \frac{AT}{OT}$Given that $OT = 4 \, cm$ and $\angle OTA = 30^{\circ}$,we substitute these values:$\cos(30^{\circ}) = \frac{AT}{4}$Since $\cos(30^{\circ}) = \frac{\sqrt{3}}{2}$,we get:$\frac{\sqrt{3}}{2} = \frac{AT}{4}$$AT = 4 	imes \frac{\sqrt{3}}{2}$$AT = 2 \sqrt{3} \, cm$.

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 $cm$):

Similar Questions

$A$ line that intersects a circle at two distinct points is called a $\ldots \ldots \ldots \ldots$ of the circle.

Prove that in two concentric circles,the chord of the larger circle,which touches the smaller circle,is bisected at the point of contact.

$\overline{PA}$ is a tangent to $\odot(O, r)$ drawn from a point $P$ outside a circle. If $m\angle AOP = 40^\circ$,then $m\angle OPA = \ldots$ (in $^\circ$)

Two concentric circles are of radii $5 \, cm$ and $3 \, cm$. Find the length of the chord of the larger circle which touches the smaller circle.

If a rhombus $ABCD$ is inscribed in a circle with center $O$ and radius $r$,then the rhombus $ABCD$ is $\ldots \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module