Circles

Q.

Number of circles that can be drawn through three non-collinear points is

1. 2

2. 3

3. 1

4. 0

Q.

ABCD is a cyclic quadrilateral, in which $\angle$DBC =80${}^{\circ }$ and $\angle$BAC = 40${}^{\circ }$ . Find $\angle$BCD.

1. 30°

2. 40°

3. 50°

4. 60°

Q. Two circles are congruent if they have equal __________ .

1. diameters
2. chords
3. radii
4. segments

Q. The part of a circle enclosed by a chord and an arc is called a:

1. Circumference
2. Segment
3. Diameter
4. Sector

Q.

Two equal chords AB and CD of a circle with centre O, when produced meet at a point E. Prove that BE = DE and AE = CE.

Q.

In the figure, O is the center of the circle. If ∠ACB = 30^o then ∠ABC equal to :

1. 15^o

2. 60^o

3. 45^o

4. 30^o

Q.

How many degrees are in one-half of a circle?

1. 180 degrees

2. 360 degrees

3. 90 degrees

4. 45 degrees

Q.

Concentric circles have same

1. radius

2. centre

3. diameter

4. circumference

Q.

Identify the following figure.

1. Rectangle

2. Circle

3. Triangle

4. Line segment

Q.

Determine the length of a chord which is at a distance of 6 cm from the centre of a circle of radius 10 cm.

1. 18 cm

2. 12 cm

3. 14 cm

4. 16 cm

Q.

Through three collinear points, a circle can be drawn.

1. True

2. False

Q.

The fixed point in a circle which is at a fixed distance from any point on the circumference is known as the _______ of the circle.

1. radius

2. center

3. circumference

4. arc

Q.

What is the angle of measure for half of revolution?

1. $60°$

2. $90°$

3. $180°$

4. $270°$

Q.

Fill in the blanks :

(i) All points lying inside / outside a circle are called ___ points / ___ points.

(ii) Circles having the same centre and different radii are called ___ circles.

(iii) A point whose distance from the centre of a circle is greater than radius lies in ___ of the circle.

(iv) A continuous piece of a circle is ___ of the circle.

(v) The longest chord of a circle is a ___ of the circle.

(vi) An arc is a ___ when its ends are the ends of a diameter.

(vii) Segment of a circle is the region between an arc and ___ of the circle.

(viii) A circle divides the plane, on which it lies, in ___ parts.

Q. Question 1 (i)
Fill in the blanks:

(i) The centre of a circle lies in the __________ of the circle. (exterior/ interior)

Q.

Prove that two different circles cannot intersect each other at more than two points.

Q. 28. Three circles touch each other externally and all the three touch a line as shown in the figure. If two of them are equal and the third has radius 2 cm , what is the radius (in cm ) of the equal circles ?

Q.

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.

(ii) A circle has only finite number of equal chords.

(iii) If a circle is divided into three equal arcs, each is a major arc.

(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.

(v) Sector is the region between the chord and its corresponding arc.

(vi) A circle is a plane figure.

Q.

Fill in the blanks

(i) The centre of a circle lies in __________ of the circle. (exterior/ interior)

(ii) A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior)

(iii) The longest chord of a circle is a __________ of the circle.

(iv) An arc is a __________ when its ends are the ends of a diameter.

(v) Segment of a circle is the region between an arc and __________ of the circle.

(vi) A circle divides the plane, on which it lies, in __________ parts.

Q. two circles with centre A and B of radii 3 and 4 cm respectively, intersect at two point P and Q such that AP and BP are †an gents of two circle .Find the length of common chord P

Q. The region between a chord and its circumference is always called

1. 
   Sector
2. 
   Major segment
3. 
   Semi- Circle
4. 
   Segment

Q. $\text{In the given figure, if}\angle POR=120°$,
$\text{then enter the value of}\angle PQR\text{in degrees.}$

1. 120

Q.

Give a geometrical construction for finding the fourth point lying on a circle passing through three given points, without finding the centre of the circle. Justify the construction.

Q. Two circles of radii 5cm and 3cm intersect at two points and the distance between their centers is 4cm . find the length of the common chord .

Q.

The maximum no. of points into which $4$ circles and $4$ straight lines intersect is :

1. $26$

2. $56$

3. $50$

4. $72$

Q.

Intersection point of perpendicular bisectors of the sides of a triangle is called ___.

Q. Question 3
Curved surface area of a cone is $308c{m}^2$ and its slant height is 14 cm. Find
(i) radius of the base.
(ii) total surface area of the cone. $[Assume\pi =\frac{22}{7}]$

Q.

What is the name of the geometric instrument used to draw arcs?

__

Q. Opposite angles of a cyclic quadrilateral are ___.

1. complementary
2. supplementary
3. equal
4. right angles

Q. In a pentagon ABCDE, AB is parallel to DC and ∠A : ∠E : ∠D = 3 : 4 : 5. Find ∠E.

1. 120°
2. 110°
3. 130°
4. 100°