P is in the exterior of odot(O, 30). The tang | vedclass

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

Question

(D) Given that $O$ is the center of the circle and $r = 30$ is the radius.Since $PQ$ is a tangent to the circle at point $Q$,the radius $OQ$ is perpen

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(D) Given that $O$ is the center of the circle and $r = 30$ is the radius.Since $PQ$ is a tangent to the circle at point $Q$,the radius $OQ$ is perpendicular to the tangent $PQ$ at the point of contact.Therefore,$	riangle OQP$ is a right-angled triangle with $\angle OQP = 90^{\circ}$.In $	riangle OQP$,by the Pythagorean theorem:$OP^2 = OQ^2 + PQ^2$Given $OP = 34$ and $OQ = r = 30$.$34^2 = 30^2 + PQ^2$$1156 = 900 + PQ^2$$PQ^2 = 1156 - 900$$PQ^2 = 256$$PQ = \sqrt{256} = 16$.Thus,the length of the tangent $PQ$ is $16$.

$P$ is in the exterior of $\odot(O, 30)$. The tangent drawn from $P$ to the circle touches the circle at $Q$. If $OP = 34$,then $PQ = \dots$

Similar Questions

Point $A$ lies in the exterior of $\odot(O, 8)$. $A$ line through $A$ touches the circle at $B$. If $AB = 15$,then find $OA$.

$A$ tangent to a circle intersects the circle in $\ldots \ldots \ldots .$

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 $cm$):

In the following figure,find the radius of the circle.

$P$ is a point in the exterior of $\odot(O, r)$ and the tangents from $P$ to the circle touch the circle at $X$ and $Y$. Find $m \angle XPO$,if $m \angle XOY = 100^\circ$. (in $^\circ$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module