(A) In the circle with center $P$,$PA = PB = 8 \ cm$ (radii of the same circle). Since $PA = PB$,$\triangle PAB$ is an isosceles triangle. Therefore,$

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

(A) In the circle with center $P$,$PA = PB = 8 \ cm$ (radii of the same circle). Since $PA = PB$,$\triangle PAB$ is an isosceles triangle. Therefore,$\angle PBA = \angle PAB = 40^{\circ}$. In $\triangle PAB$,the sum of angles is $180^{\circ}$,so $\angle APB = 180^{\circ} - (40^{\circ} + 40^{\circ}) = 100^{\circ}$. Since the chords $AB$ and $CD$ are equal and the circles have the same radius $(8 \ cm)$,the chords subtend equal angles at their respective centers. Thus,$\angle CQD = \angle APB = 100^{\circ}$.

Class 9 Mathematics Circles Mix Examples - Circles

Medium

Two circles of radii $8 \ cm$ with centers $P$ and $Q$ are given. The chord $AB$ of the circle with center $P$ and the chord $CD$ of the circle with center $Q$ are equal. If $\angle PAB = 40^{\circ}$,then find $\angle CQD$. (in $^{\circ}$)

A
$100$
B
$105$
C
$90$
D
$120$

Explore More

Browse All

Question Bank

All Subjects

Class 9 Questions

Class 9

Mathematics Questions

Chapter

Circles

Subtopic

Mix Examples - Circles

In a circle with centre $P$,the distance of a chord $AB$ from the centre $P$ is $20 \, cm$. If $AB = 96 \, cm$,then the radius of the circle is .......... $cm$.

Medium

View Solution

If $AB = 12 \, cm$,$BC = 16 \, cm$ and $AB$ is perpendicular to $BC$,then the radius of the circle passing through the points $A, B$ and $C$ is (in $cm$)

Medium

View Solution

In the figure,$AB$ and $CD$ are two equal chords of a circle with center $O$. $OP$ and $OQ$ are perpendiculars on chords $AB$ and $CD$ respectively. If $\angle POQ = 150^{\circ}$,then $\angle APQ$ is equal to: (in $^{\circ}$)

Medium

View Solution

The radius of a circle with centre $P$ is $50 \, cm$. Centre $P$ is not lying between two parallel chords $AB$ and $CD$. If $AB = 80 \, cm$ and the distance between $AB$ and $CD$ is $10 \, cm$,then find the length of $CD$. (Given $AB > CD$) (in $, cm$)

Medium

View Solution

In a circle with centre $P$,the length of a radius is $\sqrt{2} \ cm$. It is divided into two segments by chord $AB$ of length $2 \ cm$. If $C$ is a point on the major arc $AB$,then find the value of $\angle ACB$. (in $^{\circ}$)

Medium

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

Two circles of radii $8 \ cm$ with centers $P$ and $Q$ are given. The chord $AB$ of the circle with center $P$ and the chord $CD$ of the circle with center $Q$ are equal. If $\angle PAB = 40^{\circ}$,then find $\angle CQD$. (in $^{\circ}$)

Similar Questions

In a circle with centre $P$,the distance of a chord $AB$ from the centre $P$ is $20 \, cm$. If $AB = 96 \, cm$,then the radius of the circle is .......... $cm$.

If $AB = 12 \, cm$,$BC = 16 \, cm$ and $AB$ is perpendicular to $BC$,then the radius of the circle passing through the points $A, B$ and $C$ is (in $cm$)

In the figure,$AB$ and $CD$ are two equal chords of a circle with center $O$. $OP$ and $OQ$ are perpendiculars on chords $AB$ and $CD$ respectively. If $\angle POQ = 150^{\circ}$,then $\angle APQ$ is equal to: (in $^{\circ}$)

The radius of a circle with centre $P$ is $50 \, cm$. Centre $P$ is not lying between two parallel chords $AB$ and $CD$. If $AB = 80 \, cm$ and the distance between $AB$ and $CD$ is $10 \, cm$,then find the length of $CD$. (Given $AB > CD$) (in $, cm$)

In a circle with centre $P$,the length of a radius is $\sqrt{2} \ cm$. It is divided into two segments by chord $AB$ of length $2 \ cm$. If $C$ is a point on the major arc $AB$,then find the value of $\angle ACB$. (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module