# AP 9th Class Maths Bits Chapter 12 Circles with Answers

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## AP State Syllabus 9th Class Maths Bits 12th Lesson Circles with Answers

Question 1.
The point which is at equidistant from the circumference of a circle is called
A) centre
B) incentre
D) circumcentre
From the figure answer the following questions (2 and 3).

A) centre

Question 2.
If ‘O’ is the centre of the circle then AB is
B) diameter
C) semicircle
D) tangent
B) diameter

Question 3.
If AC and AD are at equidistant from’O’ then
A) AC = CO
D) AO = AC

Question 4.
Area enclosed by two radii and the arc between them is called
A) triangle
B) circle segment
C) sector
C) sector

Question 5.
Angle in the major segment of a circle is
A) Obtuse angle
B) Right angle
C) Straight angle
D) Acute angle
D) Acute angle

Question 6.
Angle in the minor segment of a circle is
A) obtuse angle
B) zero angle
C) acute angle
D) right angle
A) obtuse angle

Question 7.
A diameter divides the circle into two
A) unequal segments
B) equal segments
C) can’t say
D) none
B) equal segments

Question 8.
Let ‘O’ be the centre of a circle. The distance of chord AB from O is greater than the distance of chord CD from ‘O’ then
A) AB = CD
B) AB > CD
C) AB < CD
D) Diameter = AB + CD
B) AB > CD

Question 9.
In the figure, ‘O’ is the centre of the circle and A, AB = CD then ∠AOB =

A) ∠OAB
B) ∠OBC
C) ∠DOC
D) ∠OCD
C) ∠DOC

Question 10.
In the above figure, if ∠AOB = ∠DOC
A) AB = DC
B) AB = OC
C) DC = OA
D) AB ≠ CD
A) AB = DC

Question 11.
In the figure, the value of x is

A) 40°
B) 80°
C) 320°
D) 50°
B) 80°

Question 12.
In the above figure, if ∠C = 60° then y =
A) 40°
B) 80°
C) 240°
D) 120°
C) 240°

Question 13.
In the figure, ‘O’ is the centre of the circle, then

A) EF > CD > AB
B) EF = CD = AB
C) AB > CD > EF
D) None
C) AB > CD > EF

Question 14.
In the figure, ∠AOB = ∠COD; AB = 3 cm then CD = …………………..

A) 1.5 cm
B) 6 cm
C) 3.5 cm
D) 3 cm
D) 3 cm

Question 15.
In the figure, 0M AB and AM = 6 cm where ‘O’ is the centre of the circle then AB =

A) 6 cm
B) 12 cm
C) 3 cm
D) 6 √6 cm
B) 12 cm

Question 16.
In the figure, ∠OMA =

A) 45°
B) 90°
C) 180°
D) None
B) 90°

Question 17.
Number of points required to describe a circle is
A) one
B) two
C) three
D) infinite
C) three

Question 18.
Number of circles that can be drawn through a given point is
A) 1
B) 2
C) 3
D) many
D) many

Question 19.
Number of circles that can be drawn through two non-collinear points is
A) 2
B) 4
C) many
D) none
C) many

Question 20.
Number of circles that can be drawn through three non-collinear points is
A) 4
B) 3
C) 2
D) 1
D) 1

Question 21.

A) 45°
B) 65°
C) 25°
D) 115°
B) 65°

Question 22.
In the figure, ∠ABC is

A) 55°
B) 125°
C) 35°
D) cant be determined
B) 125°

Question 23.
If a quadrilateral is cyclic then it is a
A) parallelogram
B) convex polygon
C) rhombus
D) rectangle
D) rectangle

Question 24.
Angle subtended by an arc at its centre is ‘x°’ then, angle subtended by it at any other point on the circle is
A) $$\frac{\mathrm{x}^{\circ}}{2}$$
B) 2x°
C) x°
D) 180 – x°
A) $$\frac{\mathrm{x}^{\circ}}{2}$$

Question 25.
The perpendicular from the centre of a circle to a chord
A) bisects it
B) equals to it
C) trisects it
D) none
A) bisects it

Question 26.
The measure of the angle in a semicircle is
A) 90°
B) 180°
C) 60°
D) 45°
A) 90°

Question 27.
Angles in the same segment are
A) unequal
B) cyclic
C) equal
D) complementary
C) equal

Question 28.
The circle that passes through the vertices of a triangle is called its
A) In circle
B) Semi-circle
D) Circum circle
D) Circum circle

Question 29.
If ABCD is a cyclic quadrilateral, then ∠A + ∠C =
A) 360°
B) 180°
C) 90°
D) 120°
B) 180°

Question 30.
If the sum of the pairs of opposite angles of a quadrilateral is 180°, then the quadrilateral is
A) Cyclic
B) Symmetric
C) Eccentric
D) Genetic
A) Cyclic

Question 31.
In the given figure, the value of x is

A) 55°
B) 90°
C) 70°
D) 60°
C) 70°

Question 32.
In the given figure, ‘O’ is the centre of the circle, then the value of y is

A) 45°
B) 90°
C) 60°
D) 30°
B) 90°

Question 33.
Which part of a circle divides it into two semicircles?
B) Diameter
C) Chord
D) Secant
B) Diameter

Question 34.
Concentric circles have
A) Same centre and different radii
B) Same centre but different radii
C) Different radii but do not have the same centre.
D) Same radii but different centres
A) Same centre and different radii

Question 35.
In the given figure, if ‘O’ is the centre of the circle, then the measure of x is

A) 70°
B) 25°
C) 40°
D) 35°
D) 35°

Question 36.
The number of a non-coilinear points required to describe a circle is
A) 1
B) 2
C) 3
D) 4
C) 3

Question 37.
A cyclic rhombus is a
A) Rectangle
B) Square
C) Parallelogram
D) Trapezium
B) Square

Question 38.
A cyclic parallelogram is a
A) Square
B) Trapezium
C) Rectangle
D) Rhombus
C) Rectangle

Question 39.
The angle subtended by a semi-circle at its centre is
A) 180°
B) 90°
C) 360°
D) 120°
A) 180°

Question 40.
In the given figure, ‘O’ is the centre of the circle and OP ⊥ AB. If AP = 6 cm, then AB =

A) 3 cm
B) 9 cm
C) 12 cm
D) 18 cm
C) 12 cm

Question 41.
How many circles can be drawn through three non-collinear points?
A) 1
B) 2
C) 3
D) None of these
A) 1

Question 42.
In the given figure, arc AB = arc CD and if ∠AOB = 40°, then ∠COD =

A) 80°
B) 40°
C) 140°
D) 90°
B) 40°

Question 43.
In the given figure, ‘O’ is the centre of the circle. If ∠ACB = 35°, then ∠AOB =

A) $$\frac{1}{2}$$ ∠ACB
B) 3 ∠ACB
C) 55°
D) 2 ∠ACB
D) 2 ∠ACB

Question 44.
In the given figure, x + y =

A) 185°
B) 175°
C) 150°
D) 160°
B) 175°

Question 45.
In the given figure, ‘O’ is the centre of the circle and OP ⊥ AB. If OP = 6 cm and AP = 8 cm, then the radius of the circle is

A) 10 cm
B) 4 cm
C) 3 cm
D) 7 cm
A) 10 cm

Question 46.
An angle subtended by the arc in a semi circle is at centre is
A) 90°
B) 120°
C) 360°
D) 180°
A) 90°

Question 47.
If the length of the longest chord in a circle is 24 cins then it’s radius is ………………….
A) 12 cm
B) 24cm
C) 6 cm
D) 4 cm
A) 12 cm

Question 48.
Two circles having radii 12 cm and 5 cm touches externally then the distance between the centres of two circles is……………….
A) 7 cm
B) 12 cm
C) 5 cm
D) 17 cm
D) 17 cm

Question 49.
Let ‘O’ be the centre of circle and AB and CD’ are chords. The distance of chord AB from ‘O’ is longer than the distance of chord CD from ‘O’ then one of the following is true.
A) AB = CD
B) AB > CD
C) AB < CD D) AB + CD = 0
B) AB > CD

Question 50.
Which of the following figure represents largest angle at centre subtended by a chord. (Note : Radii are equal).

(D)

Question 51.
Given below are the lengths of chords of a circle. Among these one chord is passing through the centre. Identify the length of chord which is passing through the centre.
A) 7 cm
B) 7.5 cm
C) 8 cm
D) 6.5 cm
C) 8 cm

Question 52.
In the given figure AC is the diameter. 0 is the centre of the semi-circle. B is a point on the semi circle.
If ∠C = 48° = then ∠OBA =

A) 48°
B) 42°
C) 90°
D) 32°
B) 42°

Question 53.
In the given figure ∠CDE = 112°, then ∠AFE =
(Note : In a cyclic quadrilateral opposite angles are supplementary).

A) 112°
B) 68°
C) 78°
D) 168°
B) 68°

Question 54.
In the given circle ‘O’ is the centre. ∠ABC + ∠AOC = 2 right angles. Then ∠AOD =

A) 120°
B) 60°
C) 90°
D) 180°
B) 60°

Question 55.
The length of a chord that passes through the centre of a circle is 14 cm then what is the distance
A) 88 cm
B) 44 cm
C) 28 cm
D) 7 cm
D) 7 cm

Question 56.
Angle In a semi circle is …………………
A) Zero angle
B) Right angle
C) Straight angle
D) Complete angle
B) Right angle

Question 57.
Number of circles that can be drawn through three collinear points is ……………………
A) 0
B) 1
C) 3
D) Infinitely many