Angle Subtended by an Arc at the Center

Q.

What are the chord of a circle theorems?

Q. The measure of angle subtended by an arc at the centre of a circle is (double/ half) the measure of the angle subtended by the arc at any point on the circle.

Q.

In the adjoining figure given below, $O$ is the centre of circle, the value of $x$ is:

1. $80°$

2. $75°$

3. $70°$

4. $65°$

Q. The angle subtended by an arc at the center is half of the angle subtended by the arc at any point on the remaining part of the circle.

1. False
2. True

Q. In the given semicircle, find the angle $\angle DBE.$

1. ${7.5}^o$
2. ${15}^o$
3. ${30}^o$
4. None of the above.

Q. A triangle is formed with all its vertices lying on a circle. One of the sides of the triangle is equal to the radius of the circle. Find the angle of the triangle opposite to the side having a length equal to the circle's radius.

degrees

Q. Let two equal chords of a circle are $AX$ and $BY.$ If chord $AX$ substends ${50}^{\circ }$ at centre, then angle substends by chord $BY$ is

1. ${40}^{\circ }$
2. ${50}^{\circ }$
3. ${100}^{\circ }$
4. ${25}^{\circ }$

Q. Which of the following option is incorrect for the following figure

1. $RS=5$ cm
2. $OP=OS$
3. $RS=2$ cm
4. $OQ=OR$

Q. For the given figure, find $\angle ABC+\angle ACB,$ where $O$ is the centre of the circle.

1. ${40}^o$
2. ${120}^o$
3. ${140}^o$
4. ${180}^o$

Q. Radius of the given circle is $2cm.$ Find the ratio of the angle $\angle D$ and $\angle A.$

1. $1:1$
2. $1:2$
3. $2:1$
4. None of the above.

Q.

In the figure given below, $O$ is the centre of circle and $\angle AQR=35°$ and $\angle PAQ=120°$ then $\angle SPR$ is equal to:

1. $35°$

2. $20°$

3. $30°$

4. $25°$

Q.

In the figure, side $AC$ is extended to $D$.

$\angle BCD=\_\_\_\_\_\_\_$