(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,$

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(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 Equal Chords and their Distances from the Centre

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
$120$

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Circles

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Equal Chords and their Distances from the Centre

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 $, cm$)?

Medium

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If two equal chords of a circle intersect within the circle,prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Medium

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$AB$ and $CD$ are two chords of a circle with centre $P$. The distance of chord $AB$ from the centre $P$ is $15 \, cm$ and the distance of chord $CD$ from the centre $P$ is $8 \, cm$. If $AB = 16 \, cm$,then find the length of chord $CD$. (in $, cm$)

Medium

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In a circle with centre $P$,$AB$ and $CD$ are equal chords. If $\angle APB = 80^{\circ}$,then find $\angle CPD$. (in $^{\circ}$)

Medium

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Two chords $AB$ and $CD$ of lengths $5\, cm$ and $11\, cm$ respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between $AB$ and $CD$ is $6\, cm$,find the radius of the circle.

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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 $^{\circ}$)

Similar Questions

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 $, cm$)?

If two equal chords of a circle intersect within the circle,prove that the line joining the point of intersection to the centre makes equal angles with the chords.

$AB$ and $CD$ are two chords of a circle with centre $P$. The distance of chord $AB$ from the centre $P$ is $15 \, cm$ and the distance of chord $CD$ from the centre $P$ is $8 \, cm$. If $AB = 16 \, cm$,then find the length of chord $CD$. (in $, cm$)

In a circle with centre $P$,$AB$ and $CD$ are equal chords. If $\angle APB = 80^{\circ}$,then find $\angle CPD$. (in $^{\circ}$)

Two chords $AB$ and $CD$ of lengths $5\, cm$ and $11\, cm$ respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between $AB$ and $CD$ is $6\, cm$,find the radius of the circle.

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