Recall Arc, Central Angle and Measure of an Arc

Q. In the given figure, O is the centre of the circle. If $\angle BOC={120}^{\circ },$ then $x$ =___.

1. ${40}^{\circ }$​​​​​​​
2. ${30}^{\circ }$​​​​​​​
3. ${45}^{\circ }$​​​​​​​
4. ${60}^{\circ }$

Q.

The measure of an inscribed angle is half the measure of its in intercepted arcs.

1. True

2. False

Q.

A bicycle wheel has$24$spokes . The angle between a pair of adjacent spokes is

1. $10°$

2. $15°$

3. $24°$

4. $25°$

Q. The line bisecting the angle between two tangents drawn from a point outside the circle passes through the center of that circle.

1. True
2. False

Q. In the given figure, DC is diameter then $x$ = ___.

1. ${70}^{\circ }$
2. ${60}^{\circ }$
3. ${80}^{\circ }$
4. ${100}^{\circ }$

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

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

Q.

Fill in the blanks :

Two line segments are congruent, if they are of ______lengths.

Q.

The number of equal angles an arc subtends in the opposite segment is two.

1. False

2. True

Q. Question 10
The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal ? why?

Q. Two circles are said to be congruent if they have same _______

1. centre
2. length of chords
3. radius
4. same length of tangents

Q.

$\text{In the given figure, O is the centre of the circle. If}\angle \text{ACB}={60}^{\circ }\text{then find}\angle OAB.$

1. ${60}^{\circ }$

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

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

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

Q. is a line that touches a circle at only one point, and is a line that intersects a circle at two distinct points.

1. sector
2. Tangent
3. Arc
4. secant

Q.

O is the center and AB is a minor arc of the circle. If the angle subtended by AB at the center is $\angle$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. The line bisecting the angle between two tangents drawn from a point outside the circle passes through the center of that circle.

1. True
2. False

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

[P is any point on the circle]

1. 

2. 
3. 
4. 

Q. Question 4
In the figure, if $\angle ABC={20}^{\circ }$, then $\angle AOC$ is equal to

(A) ${20}^{\circ }$
(B) ${40}^{\circ }$
(C) ${60}^{\circ }$
(D) ${10}^{\circ }$

Q. An equilateral triangle $△EQU$ is inscribed in circle centered at O. Then m(arc EQ)=.

1. 60${}^{\circ }$
2. 90${}^{\circ }$
3. 120${}^{\circ }$
4. 150${}^{\circ }$

Q. is a line that touches a circle at only one point, and is a line that intersects a circle at two distinct points.

1. Tangent
2. Arc
3. sector
4. secant

Q.

Two line segments are said to be congruent, if they are equal in magnitude.

1. False

2. True

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 remaining part of the circle i.e. $\angle$APB is (where P is any point on the circle)?

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

2. ${45}^{\circ }$
3. ${55}^{\circ }$
4. ${65}^{\circ }$

Q. If the angles subtented by a minor arc is 30 degree, then what is the angle subtended by the major arc?

1. ${330}^{\circ }$
2. ${300}^{\circ }$
3. ${360}^{\circ }$
4. ${270}^{\circ }$

Q.

Consider two circles of radii 5 and 6 cm. Are they congruent?

1. Yes

2. Partially

3. No

4. Insufficient data

Q. Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.

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. The distance between any two parallel tangents is equal to the ___of the circle.

1. radius
2. diameter
3. circumference
4. semi circumference

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. is a line that touches a circle at only one point, and is a line that intersects a circle at two distinct points.

1. Arc
2. Tangent
3. secant
4. sector