(D) Let $r$ be the radius of the circle. For chord $AB$ of length $12 \, cm$,the distance from the centre $O$ is $d_1 = 8 \, cm$. $A$ perpendicular fr

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(D) Let $r$ be the radius of the circle. For chord $AB$ of length $12 \, cm$,the distance from the centre $O$ is $d_1 = 8 \, cm$. $A$ perpendicular from the centre to a chord bisects the chord. Thus,the distance from the centre,the radius,and half the chord length form a right-angled triangle. $r^2 = (12/2)^2 + 8^2 = 6^2 + 8^2 = 36 + 64 = 100$. So,$r = 10 \, cm$. For chord $CD$ of length $16 \, cm$,let the distance from the centre be $d_2$. $r^2 = (16/2)^2 + d_2^2$. $10^2 = 8^2 + d_2^2$. $100 = 64 + d_2^2$. $d_2^2 = 36$. $d_2 = 6 \, cm$.

Class 9 Mathematics Circles Mix Examples - Circles

Medium

In a circle with centre $O$,the lengths of two chords $AB$ and $CD$ are $12 \, cm$ and $16 \, cm$ respectively. If the chord $AB$ is at a distance $8 \, cm$ from the centre,what is the distance of the chord $CD$ from the centre (in $, cm$)?

A
$5$
B
$9$
C
$7$
D
$6$

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Mix Examples - Circles

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$AB$ and $CD$ are two parallel chords of a circle with centre $P$. Also,the centre $P$ lies between $AB$ and $CD$. If $AB = 48 \, cm$,$CD = 40 \, cm$,and the radius of the circle is $25 \, cm$,find the distance between $AB$ and $CD$. (in $, cm$)

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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 $, cm$)

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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 $^{\circ}$)

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In a circle with centre $O$,the lengths of two chords $AB$ and $CD$ are $12 \, cm$ and $16 \, cm$ respectively. If the chord $AB$ is at a distance $8 \, cm$ from the centre,what is the distance of the chord $CD$ from the centre (in $, cm$)?

Similar Questions

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 $^{\circ}$)

$AB$ and $CD$ are two parallel chords of a circle with centre $P$. Also,the centre $P$ lies between $AB$ and $CD$. If $AB = 48 \, cm$,$CD = 40 \, cm$,and the radius of the circle is $25 \, cm$,find the distance between $AB$ and $CD$. (in $, cm$)

In the given figure,$ABCD$ is a cyclic quadrilateral in which diagonals $AC$ and $BD$ intersect at $M.$ If $\angle BAC = 50^{\circ}$ and $\angle ADB = 45^{\circ}$,then find $\angle ABC$. (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 $, cm$)

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 $^{\circ}$)

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