Circle and Its Parts

Q.

If ABCD is a cyclic quadrilateral with AB as the diameter of the circle and $\angle ACD={50}^{\circ },$ then $\angle BAD$ = ___.

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

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

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

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

Q. Radius of a circle is 17 cm. If length of the chord is 30 cm, then find its distance from the centre.

1. 8

Q. Where do any two diameters of a circle always intersect ?

1. On the circle
2. At the center of the circle
3. They never intersect
4. At a point outside the circle.

Q. Question 2 (i)
Write True or False. Give reasons for your answers.

(i) Line segment joining the centre to any point on the circle is a radius of the circle

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

1. ${30}^{\circ }$
2. ${20}^{\circ }$
3. ${10}^{\circ }$
4. ${40}^{\circ }$

Q.

When a circle and a line are in a plane, they can have only two points of intersection.

1. True

2. False

Q. Question 2 (i)
Write True or False. Give reasons for your answers.

(i) Line segment joining the centre to any point on the circle is a radius of the circle

Q. A wheel of radius $\frac{4}{\pi }$ cm touches a flat surface. What is the distance covered by the wheel in one complete rotation?

1. 4 cm
2. 8 cm
3. 2 cm
4. 6 cm

Q. A chord of a circle which is twice the radius of the circle is the diameter of the circle.

1. True
2. False

Q. If the radius of a circle gets increased by 10%, then what is the percentage increase in its diameter?

1. 40%
2. 20%
3. Remains same
4. 10%

Q.

A bicycle wheel has a diameter of $7cm.$ What distance does the wheel cover on the ground if it completes 1 full rotation?

$(\text{Take}\pi =\frac{22}{7})$

1. $44cm$

2. $22cm$

3. $21cm$

4. $42cm$

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

Q. How many secants can be drawn on a circle?

Q.

Identify the major sector and minor segment in the given figure:

1. OACB, OADB

2. ABDA, ACBA

3. OADB, ACBA

4. OACB, ADBA

Q.

If AB is a chord which passes through the centre O of a circle, then what is AB known as?

1. Radius of the circle

2. Diameter of the circle

3. Segment of the circle

4. Sector of the circle

Q. Match the following circle with the given radius with their circumference.

1. 44 cm
2. 22 cm
3. 66 cm
4. 110 cm

Q.

A circle has radius 2 cm. What is the length of its longest chord?

1. 2 cm

2. 5 cm

3. 16 cm

4. 4 cm

Q. Identify the major segment in the image.(Tap on the correct color)

1. 
2. 
3. 

Q.

Which of the given line segments is a radius of the given circle?

1. OA

2. PQ

3. MN

4. None of these

Q.

The ratio of radius to diameter of a circle is _____.

1. 1 : 4

2. 1 : 2

3. 2 : 1

4. 4 : 1

Q. In the given figure, $O$ is the centre of the circle and $\angle BCO={30}^o$. Find $x$ and $y$.

Q. In the given figure, $AB$ and $CD$ are straight lines through the
centre $O$ of a circle. If $\angle AOC={80}^o$ and $\angle CDE={40}^o$, find $\angle ABC$

Q. In the given figure, $AB$ is a chord of a circle with center $O$ and $AB$ is produced to $C$ such that $BC=OB$. Also, $CO$ is joined and produced to meet the circle in $D$. If $\angle ACD=y^o$ and $\angle AOD=x^o$, prove that $x=3y$

Q. In the given figure, $O$ is the centre of the circle and $\angle AOB={70}^o$. Calculate the value of $\angle OAC$.

Q. In the given figure, O is the center of the circle BD = OD and $CD\perp AB$. Find $\angle CAB$ (in degrees)