(D) According to the circle theorem,the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part

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(D) According to the circle theorem,the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.Here,the arc $AB$ subtends $\angle APB$ at the centre $P$ and $\angle ACB$ at the point $C$ on the major arc.Therefore,$\angle APB = 2 \times \angle ACB$.Given $\angle ACB = 47^{\circ}$.So,$\angle APB = 2 \times 47^{\circ} = 94^{\circ}$.

Class 9 Mathematics Circles Mix Examples - Circles

Medium

In a circle with centre $P$,$AB$ is a chord and point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle ACB = 47^{\circ},$ then $\angle APB = $ .......... (in $^{\circ}$)

A
$47$
B
$84$
C
$112$
D
$94$

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Mix Examples - Circles

Write True or False and justify your answer in each of the following:
Two chords $AB$ and $AC$ of a circle with centre $O$ are on the opposite sides of $OA$. Then $\angle OAB = \angle OAC$.

Easy

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If circles are drawn taking two sides of a triangle as diameters,prove that the point of intersection of these circles lies on the third side.

Medium

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Write True or False and justify your answer in each of the following:
In the figure,if $AOB$ is a diameter and $\angle ADC = 120^{\circ}$,then $\angle CAB = 30^{\circ}$.

Medium

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$ABCD$ is a parallelogram. $A$ circle through $A$ and $B$ is drawn such that it intersects $AD$ at $P$ and $BC$ at $Q$. Prove that $P, Q, C,$ and $D$ are concyclic.

Medium

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Prove that among all the chords of a circle passing through a given point inside the circle,the one that is perpendicular to the diameter passing through the point is the smallest.

Easy

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In a circle with centre $P$,$AB$ is a chord and point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle ACB = 47^{\circ},$ then $\angle APB = $ .......... (in $^{\circ}$)

Similar Questions

Write True or False and justify your answer in each of the following:Two chords $AB$ and $AC$ of a circle with centre $O$ are on the opposite sides of $OA$. Then $\angle OAB = \angle OAC$.

If circles are drawn taking two sides of a triangle as diameters,prove that the point of intersection of these circles lies on the third side.

Write True or False and justify your answer in each of the following:In the figure,if $AOB$ is a diameter and $\angle ADC = 120^{\circ}$,then $\angle CAB = 30^{\circ}$.

$ABCD$ is a parallelogram. $A$ circle through $A$ and $B$ is drawn such that it intersects $AD$ at $P$ and $BC$ at $Q$. Prove that $P, Q, C,$ and $D$ are concyclic.

Prove that among all the chords of a circle passing through a given point inside the circle,the one that is perpendicular to the diameter passing through the point is the smallest.

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Write True or False and justify your answer in each of the following:
Two chords $AB$ and $AC$ of a circle with centre $O$ are on the opposite sides of $OA$. Then $\angle OAB = \angle OAC$.

Write True or False and justify your answer in each of the following:
In the figure,if $AOB$ is a diameter and $\angle ADC = 120^{\circ}$,then $\angle CAB = 30^{\circ}$.