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Standard IX

Mathematics

Angle Subtended by an Arc of a Circle on the Circle and at the Center

In the given ...

Question

In the given figure, A, B and C are three points on a circle with centre O such that ∠BOC = 30° and ∠AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.

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Solution

It can be observed that

∠AOC = ∠AOB + ∠BOC

= 60° + 30°

= 90°

We know that angle subtended by an arc at the centre is double the angle subtended by it any point on the remaining part of the circle.

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Similar questions

Q. In the figure

A, B

and

C

are three points on a circle with centre

O

such that

∠ B O C = 30^{o}

and

∠ A O B = 60^{o}

. If

D

is a point on the circle other than the arc

A B C

, find

∠ A D C

Q. In the given figure A, B and C are three points on a circle with centre O such that

∠ B O C = 30^{\circ}

and

∠ A O B = 60^{\circ}

. If D is a point on the circle other than the arc ABC, find

∠ A D C

in degrees.

Q. Question 1
In the given figure A, B and C are three points on a circle with centre O such that $\angle BOC = 30^{\circ}$ and $\angle AOB = 60^{\circ}$. If D is a point on the circle other than the arc ABC, find $\angle ADC$.

In the given figure, $A, B$ and $C$ are three points on a circle with centre $O$ such that $∠ B O C = 30^{\circ}$ and $∠ A O B = 60^{\circ}$ . If $D$ is a point on the circle other than the arc $A B C,$ find $∠ A D C$ .

In the given figure, A, B and C are three points on the circle with centre O such that $∠ B O C = 30^{\circ}$ and $∠ A O B = 60^{\circ}$ . If D is a point on the circle that is not on the arc ABC, then find $∠ A D C .$

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In the given figure, A, B and C are three points on a circle with centre O such that ∠BOC = 30° and ∠AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.

It can be observed that ∠AOC = ∠AOB + ∠BOC = 60° + 30° = 90° We know that angle subtended by an arc at the centre is double the angle subtended by it any point on the remaining part of the circle.

It can be observed that

∠AOC = ∠AOB + ∠BOC

= 60° + 30°

= 90°

We know that angle subtended by an arc at the centre is double the angle subtended by it any point on the remaining part of the circle.