(D) We know that the radius of a circle is perpendicular to the tangent at the point of contact.Therefore,$OP \perp PQ$.This forms a right-angled tria

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

(D) We know that the radius of a circle is perpendicular to the tangent at the point of contact.Therefore,$OP \perp PQ$.This forms a right-angled triangle $\triangle OPQ$,where $OP = 5 \, cm$ (radius) and $OQ = 12 \, cm$ (hypotenuse).By applying the Pythagoras theorem in $\triangle OPQ$:$OP^2 + PQ^2 = OQ^2$$5^2 + PQ^2 = 12^2$$25 + PQ^2 = 144$$PQ^2 = 144 - 25$$PQ^2 = 119$$PQ = \sqrt{119} \, cm$.

Class 10 Mathematics Circles Textbook - Circles

Medium

$A$ tangent $PQ$ at a point $P$ of a circle of radius $5 \, cm$ meets a line through the centre $O$ at a point $Q$ so that $OQ = 12 \, cm$. The length of $PQ$ is (in $cm$):

A
$12$
B
$13$
C
$8.5$
D
$\sqrt{119}$

Explore More

Browse All

Question Bank

All Subjects

Class 10 Questions

Class 10

Mathematics Questions

Chapter

Circles

Subtopic

Textbook - Circles

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Medium

View Solution

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.

Medium

View Solution

Draw a circle and two lines parallel to a given line such that one is a tangent and the other is a secant to the circle.

Medium

View Solution

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

Easy

View Solution

$PQ$ is a chord of length $8 \, cm$ of a circle of radius $5 \, cm$. The tangents at $P$ and $Q$ intersect at a point $T$ (see figure). Find the length $TP$.

Difficult

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ tangent $PQ$ at a point $P$ of a circle of radius $5 \, cm$ meets a line through the centre $O$ at a point $Q$ so that $OQ = 12 \, cm$. The length of $PQ$ is (in $cm$):

Similar Questions

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

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.

Draw a circle and two lines parallel to a given line such that one is a tangent and the other is a secant to 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.

$PQ$ is a chord of length $8 \, cm$ of a circle of radius $5 \, cm$. The tangents at $P$ and $Q$ intersect at a point $T$ (see figure). Find the length $TP$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module