(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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In a circle with centre $P$,the diameter of the circle is $70 \, cm$. The chord $AB$ is at a distance of $21 \, cm$ from the centre of the circle,then $AB = \dots \, cm$.

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In a circle with centre $P$,the length of chord $AB$ is $40 \, cm$. $AB$ lies at a distance of $21 \, cm$ from the centre $P$. Find the diameter of the circle. (in $, cm$)

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$AB$ is a chord of a circle with centre $P$. Point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle ACB = 50^{\circ}$,then find $\angle APB$. (in $^{\circ}$)

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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

In a circle with centre $P$,the diameter of the circle is $70 \, cm$. The chord $AB$ is at a distance of $21 \, cm$ from the centre of the circle,then $AB = \dots \, cm$.

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

$AB$ and $XY$ are two chords of a circle whose centre is $P$. $A$ line $l$ passing through the centre $P$ bisects chords $AB$ and $XY$ both. Prove that $AB \parallel XY$.

In a circle with centre $P$,the length of chord $AB$ is $40 \, cm$. $AB$ lies at a distance of $21 \, cm$ from the centre $P$. Find the diameter of the circle. (in $, cm$)

$AB$ is a chord of a circle with centre $P$. Point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle ACB = 50^{\circ}$,then find $\angle APB$. (in $^{\circ}$)

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