# Circles

## Trending Questions

**Q.**

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

2

3

1

0

**Q.**

ABCD is a cyclic quadrilateral, in which ∠DBC =80∘ and ∠BAC = 40∘ . Find ∠BCD.

30°

40°

50°

60°

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

- diameters
- chords
- radii
- segments

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

- Circumference
- Segment
- Diameter
- 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^{ }:

15

^{o}60

^{o}45

^{o}30

^{o}

**Q.**

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

180 degrees

360 degrees

90 degrees

45 degrees

**Q.**

Concentric circles have same

radius

centre

diameter

circumference

**Q.**

Identify the following figure.

Rectangle

Circle

Triangle

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.

18 cm

12 cm

14 cm

16 cm

**Q.**

Through three collinear points, a circle can be drawn.

True

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.

radius

center

circumference

arc

**Q.**

What is the angle of measure for half of revolution?

$60\xb0$

$90\xb0$

$180\xb0$

$270\xb0$

**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

Sector

Major segment

Semi- Circle

Segment

**Q.**In the given figure, if ∠POR=120°,

then enter the value of ∠PQR in degrees.

- 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 :

$26$

$56$

$50$

$72$

**Q.**

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

**Q.**

**Question 3**

Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find

(i) radius of the base.

(ii) total surface area of the cone. [Assume π=227]

**Q.**

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

**Q.**Opposite angles of a cyclic quadrilateral are ___.

- complementary
- supplementary
- equal
- right angles

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

- 120°
- 110°
- 130°
- 100°