Angles in the Same Arc Are Equal

Q.

In fig., A, B and C are points on OP, OQ and OR respectively such that AB $\parallel$ PQ and AC$\parallel$ PR. Show that BC $\parallel$ QR.

Q.

Find the value of x + y in the figure given below:

1. ${70}^{\circ }$

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

3. ${62}^{\circ }$

4. ${75}^{\circ }$

Q. A chord of radius $12cm$ subtends an angle of ${120}^{\circ }$ at the centre. Find the area of corresponding segment of the circle. $(22/7=3.14$ and root $3=1.73)$.

Q.

Calculate the angles D and B of the quadrilateral shown in the figure.

Q. $AB$ is the diameter of a circle, center $C$. $P$ is a point on the circumference. Calculate the angle $a^o$.

1. ${90}^o$
2. ${43}^o$
3. ${34}^o$
4. ${138}^o$

Q.

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

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

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

3. ${50}^{\circ }$

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

Q.

In the figure below, AB and AC are chords of the circle and OP and OQ are radii parallel to them:

Find the ratio of $\angle BOC$ and $\angle POQ$ .

Q. Angle subtended by one of the equal chords at centre is 60 degrees, angle made by other chord is:

1. 60 degrees
2. 12 degrees
3. 30 degrees
4. 45 degrees

Q.

If one angle of a cyclic quadrilateral measures 100 degrees, then its opposite angle measures

1. 90 degrees

2. 80 degrees

3. 100 degrees

4. 120 degrees

Q.

The angle subtended by an arc on the circumference is 80 degrees. The angle subtended by it at the centre is

1. 120 degrees

2. 100 degrees

3. 160 degrees

4. 130 degrees