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

Q. If ∠𝑂𝐴𝐵 = 40° and 𝐴𝐵 = 𝐶𝐷, then find the measure of ∠𝐶𝑂𝐷.

$\left[2Marks\right]$

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. ${90}^{\circ }$

2. ${100}^{\circ }$

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

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

Q.

An equilateral triangle ABC is inscribed in a circle with centre O. Then, $\angle BOC$ is equal to:

1. 30°

2. 60°

3. 90°

4. 120°

Q.

A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc.

1. ${150}^{\circ },{30}^{\circ }$

2. ${120}^{\circ },{60}^{\circ }$

3. ${30}^{\circ },{150}^{\circ }$

4. ${60}^{\circ },{120}^{\circ }$

Q.

O is the centre of the circle. AB is a minor arc of the circle. The angle subtended by AB at centre $\angle$AOB = ${110}^{\circ }$, then angle subtended by the arc at any point on the circle $\angle$APB is, where P is any point on the circle?

1. 
2. 

3. 

4. 

Q. In fig., if $<OAB={40}^{\circ }$, the < ACB is equal to:

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

Q.

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

1. 50°

2. 40°

3. 30°

4. 20°

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. ${55}^{\circ }$

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

3. $(\frac{60}{2}{)}^{\circ }$

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

Q.

In the given figure, $\angle PQR={100}^{\circ }$, where P, Q and R are points on a circle with centre O. Find $\angle OPR$.

1. ${20}^{\circ }$

2. ${10}^{\circ }$

3. ${40}^{\circ }$

4. ${80}^{\circ }$

Q.

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

1. 80°

2. 150°

3. 50°

4. 40°