Angle Subtended by an Arc of a Circle at the Centre

Q.

In the given figure, if $\angle \text{OAB}={40}^{\circ }$, then $\angle \text{ACB}$ = ___.

1. ${40}^{\circ }$

2. ${50}^{\circ }$

3. ${70}^{\circ }$

4. ${60}^{\circ }$

Q. In the given figure, if $\angle \text{OAB}={30}^{\circ }$, then $\angle \text{ACB}$ = ___.

1. ${30}^{\circ }$
2. ${60}^{\circ }$
3. ${40}^{\circ }$
4. ${50}^{\circ }$

Q. Question 9
Write True or False and justify your answer :

If A, B, C and D are four points such that $\angle BAC={45}^{\circ }$ and $\angle BDC={45}^{\circ }$ , then A, B, C, D are concyclic.

Q. Question 6
ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. Prove that $\angle CBD+\angle CDB=\frac{1}{2}\angle BAD$.

Q. In the given figure, what is the value of x?

1. ${10}^{\circ }$
2. ${30}^{\circ }$
3. ${15}^{\circ }$
4. ${20}^{\circ }$

Q. Question 6
In the figure, if $\angle OAB={40}^{\circ }$, the $\angle ACB$ is equal to


(A) ${50}^{\circ }$
(B) ${40}^{\circ }$
(C) ${60}^{\circ }$
(D) ${70}^{\circ }$

Q. In the figure below, O is the centre of the circle and $\angle QPR=x^{\circ },\angle ORQ=y^{\circ }.$ Which statement is true about $x^{\circ }$ and $y^{\circ }$?

1. $x^{\circ }+y^{\circ }={120}^{\circ }$
2. $x^{\circ }+y^{\circ }={180}^{\circ }$
3. $x^{\circ }+y^{\circ }={90}^{\circ }$
4. $x^{\circ }+y^{\circ }={150}^{\circ }$

Q. In the figure, if $\angle OAB={40}^{\circ }$, $\angle ACB$ is equal to

1. ${50}^{\circ }$
2. $\frac{1}{2}\angle AOB$
3. ${60}^{\circ }$
4. ${70}^{\circ }$

Q.

In the given figure $\angle$ AOC=${130}^{\circ }$, The value of $\angle$ ABC (in degrees) is _______.

1. ${95}^{\circ }$

2. ${115}^{\circ }$

3. $50\circ$

4. ${100}^{\circ }$

Q. O is the centre of the circle as shown in the figure. If $\angle ORP={35}^{\circ }$ and the distance between P and Q through 'O' is 4 cm, then what is the measure of $\angle ROQ$ ?

1. ${55}^{\circ }$
2. ${35}^{\circ }$
3. ${70}^{\circ }$
4. ${105}^{\circ }$

Q.

In the figure, if $\angle OAB={40}^{\circ }$, $\angle ACB$ is equal to

1. ${50}^{\circ }$

2. $\frac{1}{2}\angle AOB$

3. ${60}^{\circ }$

4. ${70}^{\circ }$

Q. Question 6
ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. Prove that $\angle CBD+\angle CDB=\frac{1}{2}\angle BAD$.

Q.

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 $\angle ADC$.

1. $\frac{1}{2}\angle AOC$
   

2. ${45}^{\circ }$

3. $\frac{1}{2}\angle AOB$

4. ${30}^{\circ }$

Q.

Given a circle with $O$ as the centre. Find the value of $x$.

1. 80°

2. 150°

3. 50°

4. 40°

Q. ABCD is a quadrilateral such that A is the centre of the circle passing through B, C and D. Which one of the following options is correct?

1. $\angle CBD+\angle CDB=\angle BAD$
2. $\angle CBD+\angle CDB=\frac{1}{2}\angle BAD$
3. $\angle CBD+\angle CDB=\frac{3}{4}\angle BAD$
4. $\angle CBD+\angle CDB=\frac{2}{3}\angle BAD$

Q. $PQ$ is the diameter of a semicircle with radius $4cm$ and $\angle PRQ$ is the angle on the semicircle. If $QR=2\sqrt{7}cm$, then length of $PR$ is :

1. $5cm$
2. $6cm$
3. $2\sqrt{11}cm$
4. $8cm$

Q. In figure, if $\angle OAB={40}^{\circ }$, then $\angle ACB$ is equal to ___.

1. ${50}^{\circ }$
2. ${40}^{\circ }$
3. ${70}^{\circ }$
4. ${60}^{\circ }$

Q.

In 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.

1. 60°

2. 45°

3. 30°

4. 90°

Q. Question 16
In figure, $\angle ACB={40}^{\circ }$. Find $\angle OAB$.

Q.
If $\angle ACB={40}^{\circ },$ then what is the value of $x$?

1. ${50}^{\circ }$
2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${80}^{\circ }$

Q. In the given figure, O is the centre of the circle. A is any point on minor arc BC. Find the value of $\angle BAC-\angle OBC$.

1. ${90}^{\circ }$
2. ${120}^{\circ }$
3. ${60}^{\circ }$
4. ${45}^{\circ }$

Q.

In the given figure $\angle$ AOC = ${130}^{\circ }$, The value of $\angle$ ABC (in degrees) is _______.

1. 95

2. 115

3. 50

4. 100

Q. In the given figure, PQ is the diameter of a circle with centre O. If $\angle PQR={65}^o,\angle SPR={40}^o$ and $\angle PQM={50}^o$. Find (i) $\angle QPR$ (ii) $\angle QPM$ and (iii) $\angle PRS.$

Q. In the given figure, O is the centre of a circle and PQ is a diameter. If $\angle ROS={40}^{\circ },$ then what is the value of $\angle RTS$?

1. ${20}^{\circ }$
2. ${45}^{\circ }$
3. ${70}^{\circ }$
4. ${65}^{\circ }$

Q.

BC is chord of a circle with centre O. A is a point on major arc BC. Find the total measure of $\angle BAC$ and $\angle OBC$.

1. ${100}^{\circ }$

2. ${90}^{\circ }$

3. ${120}^{\circ }$

4. ${150}^{\circ }$

Q. In the given figure, O is the centre of the circle. Tap on the angle whose value will be $2x^{\circ }.$

1. 
2. 
3. 
4. 

Q. Consider the figure where $\angle AOB={90}^{\circ }$ and $\angle ABC={30}^{\circ }.$ Then, $\angle CAO$ = ___.

1. ${75}^{\circ }$
2. ${60}^{\circ }$
3. ${45}^{\circ }$
4. ${50}^{\circ }$

Q. In the given figure, $O$ is the centre of circle. If $\angle AOD={140}^o$ and $\angle CAB={50}^o$, calculate
$\angle EDB$

Q.
If $\angle COD={80}^{\circ },$ then $\angle CAD$ = ___.

1. $\angle CBD$
2. ${40}^{\circ }$
3. ${160}^{\circ }$
4. $\angle COB$

Q.

In the given figure, O is the centre of the circle. Find $x$.

1. ${50}^{\circ }$

2. ${40}^{\circ }$

3. ${30}^{\circ }$

4. ${20}^{\circ }$