#Class 9 #MCQ #Chapter_10 #Circles

Maths Learning Centre, Jalandhar
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https://www.youtube.com/@MathematicsOnlineLectures Class IX: Circles Mathematics
MULTIPLE CHOICE QUESTIONS
LEVEL - I
1. The centre of the circle lies
(A) exterior (B) Interior (C) on the circle (D) None of these
2. A circle has how many chords
(A) Finite (B) Infinite (C) One (D) Two
3. The longest chord of a circle is
(A) radius (B) diameter (C) circum centre (D) None of these
4. Angles in semi circle is
(A) right angle (B) acute angle (C) obtuse angle (D) None of these
5. The radius of the circle, whose diameter is 20 cm
(A) 5 cm (B) 10 cm (C) 15 cm (D) 20 cm
6. The diameter of the circle whose radius is 5 cm
(A) 5 cm (B) 15 cm (C) 10 cm (D) 20 cm
7. The length of a chord which is at a distance of 5 cm from the centre of a circle of radius 13 cm
(A) 13 cm (B) 15 cm (C) 24 cm (D) 14 cm
8. If radius are different, centre is same then circle is
(A) semi circle (B) concentric circle (C) point circle (D) None of these
9. The mid point of diameter is
(A) centre (B) radius (C) diameter (D) None of these
10. The minimum number of points the circle is passing through
(A) 4 (B) 1 (C) 3 (D) 2
11. ABC withAB = AC = 10 cm and BC = 12 cm has been inscribed in a circle. Then the radius of the
circle is
(A) 6.25 cm (B) 8 cm (C) 10 cm (D) 10.2 cm
12. PQ and RS are two parallel chords of a circle whose centre is O and radius is 10 cm. If PQ = 16 cm
and RS = 12 cm, if they lie on the same side of the centre O then the distance between PQ and RS
(A) 3 cm (B) 2 cm (C) 4 cm (D) 5 cm
13. The radius of the circle is 13 cm and the length of the chord is 10 cm then the distance from the
chord from the centre is
(A) 10 cm (B) 12 cm (C) 14 cm (D) 18 cm
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14. The length of a chord which is at a distance of 12 cm from the centre of a circle of radius 13 cm is
(A) 20 cm (B) 22 cm (C) 10 cm (D) 12 cm
15. The radius of a circle in which a longest chord of the circle is of length 10.6 cm is
(A) 5.3 cm (B) 5.8 cm (C) 5.1 cm (D) 5 cm
16. In figure, ABC = 69°, ACB = 31°, then BDC is
31°
D
A
B C
69°
(A) 70o
(B) 90o
(C) 80o
(D) 120o
17. Two circles intersect at two points A and B. AD and AC are diameters to the two circles (fig.). then
B lies on the line segment
D
A
B C
(A) AB (B) BC (C) CD (D) None of these
18. Two circles intersect in A and B and AC and AD are respectively the diameters of the circles.
C, B, D are
D
A
B
C
O
O
(A) collinear (B) non-collinear (C) cyclic (D) None of these

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19. ABC and ADC are two right triangles with common hypotenuse
AC. Then CAD =
(A) BCD
D
A B
C
O
(B) BAD
(C) CBD
(D) ACB
20. If one side of a cyclic quadrilateral is produced, then the exterior
angle is equal to the
(A) interior angle
D
A B
C
O
E
(B) interior opposite angle
(C) exterior angle
(D) exterior opposite angle
21. A, B, C and D, E, F are two sets of collinear points. then
AD parallel to
(A) CF
B
A
E F
C
D
1
3
2
(B) DE
(C) AB
(D) BE
22. In the given figure, BOC is a diameter of a circle and AB = AC.
Then, ABC = ?
(A) 30o
(B) 45o
(C) 60o
(D) 90o
23. In the given figure, O is the centre of a circle and
ACB = 30o
. Then,  AOB = ?
(A) 30o
O
C
A B
30o
(B) 15o
(C) 60o
(D) 90o
24. In the given figure, O is the centre of a circle. If
OAB = 40o
and C is a point on the circle, then ACB =?
(A) 40o
O
C
A
B
40o
(B) 50o
(C) 80o
(D) 100o

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25. In the given figure, AOB is a diameter of a circle with centre O
such that AB = 34 cm and CD is a chord of length 30 cm. Then,
the distance of C from AB is
(A) 8 cm
(B) 15 cm
(C) 18 cm
(D) 6 cm
26. In the given figure, O is the centre of a circle and diameter AB
bisects the chord CD at a point E such that CE = ED = 8 cm and
EB = 4 cm. The radius of the circle is
(A) 10 cm A
O B
D
C
E
(B) 12 cm
(C) 6 cm
(D) 8 cm
27. An equilateral triangle of side 9 cm is inscribed in a circle. The radius of the circle is
(A) 3 cm (B) 3 2cm (C) 3 3cm (D) 6 cm
28. Angles in the same segment of a circle area are
(A) equal (B) complementary (C) supplementary (D) none of these
29. In the given figure, ABCD is a rectangle inscribed in a quadrant of
a circle of radius 10 cm. If AD = 2 5 cm, then area of the
rectangle is
(A) 32 cm2
A B E
C
F
D
10
cm
2
5
cm
Ö
(B) 40 cm2
(C) 44 cm2
(D) 48 cm2
30. In the given figure, BOC is a diameter of a circle with centre O. If
AB and CD are two chords such that AB || CD. If AB = 10 cm,
then CD = ?
(A) 5 cm
(B) 12.5 cm
(C) 15 cm
(D) 10 cm
31. In a circle of radius 5 cm, AB and AC are two chords such that AB = AC = 6 c. The perpendicular
distance of A from BC is
(A) 3.6 cm (B) 4 cm (C) 3 cm (D) 6 cm
32. Angle in a semicircle is
(A)halfright angle (B) two right angles (C) threeright angles (D) aright angle
33. Equalchords ofa circle subtend:
(A) unequalangles (B) equalangles at the center
(C) smaller angles (D) bigger angles at the center

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LEVEL - II
1. AB and CD are two equal chords of a circle with centre O such
that AOB = 80o
, then  COD = ?
(A) 100o
(B) 80o
(C) 120o
(D) 40o
2. In Figure, AB = CB and O is the centre of the circle. Then the BO
bisects
(A) ABC
B
A
O
C
(B) AOB
(C) AOC
(D) BOC
3. In the given figure, CD is the diameter of a circle with centre O
and CD is perpendicular to chord AB. If AB = 12 cm and
CE = 3 cm, then radius of the circle is
(A) 6 cm
(B) 9 cm
(C) 7.5 cm
(D) 8 cm
4. PQ and RQ are chords of a circle equidistant from the centre. The diameter passing through Q
bisects
(A) PQR (B) PRQ (C) PRQ (D) None of these
5. Two chords AC and BC subtends angles 55o
and 155o
respectively at the centre O of the circle, then
ACB is
(A) 80o
(B) 90o
(C) 75o
(D) 85o
6. AB is a chord of a circle having centre at O. If AOB=60º, then
the chord AB is equal to
(A) radius length
O
A B
60º
r r
(B) diameter length
(C) half radius length
(D) None of these
7. In figure O is the centre of the circle. If chord AP=chord PB, then
OP is bisector of
(A) AOB
O
A B
P
(B) POA
(C) POB
(D) None of these

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8. The length of a chord of a circle which is at a distance of 6 cm
from the centre of the circle. Then the length of the chord is
(A) 20 cm
A M B
O
6cm
10cm
(B) 16 cm
(C) 15 cm
(D) 25 cm
9. In figure O is the centre of the circle, OLAB and OMCB. If
OAB = OCB, Then AB=
(A) AO
O
B
C
A
L M
(B) BO
(C) CB
(D) AC
10. In the given figure, AB is a chord of a circle with centre O and AB
is produced to C such that BC = OB. Also, CO is joined and
produced to meet the circle in D. If  ACD = 25o
, then
AOD = ?
(A) 50o
(B) 75o
(C) 90o
(D) 100o
11. In the given figure, AB is a chord of a circle with centre O and
BOC is a diameter. If OD  AB such that OD = 6 cm, then
AC = ?
(A) 9 cm
(B) 12 cm
(C) 15 cm
(D) 7.5 cm
12. In the given figure, ABC and DBC are inscribed in a circle
such that BAC = 60o
and DBC = 50o
. Then, BCD = ?
(A) 50o
(B) 60o
(C) 70o
(D) 80o
13. In the given figure, BOC is a diameter of a circle with centre O.
If BCA = 30o
, then CDA = ?
(A) 30o
(B) 45o
(C) 60o
(D) 50o

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14. In the given figure, O is the centre of a circle. If OAC = 50o
, then
OBD is
(A) 40o
(B) 50o
(C) 60o
(D) 75o
15. In the given figure, O is the centre of a circle in which
OBA = 20o
and OCA = 30o
. Then, BOC = ?
(A) 50o
(B) 90o
(C) 100o
(D) 130o
16. In the given figure, O is the centre of a circle. If AOB = 100o
and AOC = 90o
, then BAC = ?
(A) 85o
(B) 80o
(C) 95o
(D) 75o
17. In the diagram, O is the center of the circle. The angles CBD is
equal to –
(A) 25°
50
o
O
A
B
D
C
(B) 50°
(C) 60o
(D) 75o
18. In figure,  DAB = 70 and  ABD = 40 , the  ACB is
equal to:
(A) 40
70o
40
o
A
D
C
B
(B) 70
(C) 110
(D) 30
19. In the given fig, O is the centre of the circle and DAB = 50o
,
then x is equal to
(A) 50o O
D
C
B
A
xo
50o
(B) 65o
(C) 100o
(D) 130o

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20. In the given fig; BAD = 75o
, then x is equal to:
(A) 75o
D E
A
B C
F
75
o
x
o
(B) 105o
(C) 25o
(D) 15o
21. AB and CD are two parallel chords of a circle (lying on opposite sides of the center) such that
AB = 16 cm and CD = 12 cm. If the distance between AB and CD is 14 cm, the radius of the
circle is
(A) 10 cm (B) 12 cm (C) 14 cm (D) 17 cm
22. The circle graph represents a total of 240 animals. The shaded
area represents the number of monkeys. How many of the animals
are monkeys?
(A) 8 330o
Monkeys
(B) 20
(C) 30
(D) 72
23. The wheel rim has a diameter of 15 metres. Which of the following
is closest to the inside circumference of the tyre designed to fit on
the rim. ?
(A) 94.2 m
(B) 176.6m
(C) 706.6 m
(D) 47.1 m
MATRIX MATCHING
This section contains Matrix-Match Type questions. Each question contains statements given in two
columns which have to be matched. Statements (A, B, C, D) in Column–I have to be matched with
statements (p, q, r, s) in Column–II.
24.
S
E
V
G
A M
N
U
J
R
Column–I Column–II
(A) Radius of interior concentric circle (p) Segment RE
(B) Chord of exterior concentric circle (q) Segment RA
(C) Radius of exterior concentric circle (r) Segment MS
(D) An acute central angle (s) Angle NRM
(A) (A-s), (B-r), (C-q), (D-p) (B) (A-q), (B-r), (C-s), (D-p)
(C) (A – q), (B – r), (C – p), (D – s) (D) (A-r), (B-p), (C-q), (D-s)

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25. For figure Shown, PQR = 100°, where P, Q and R are points on a circle with center O. Column
II give value of angle given in column I. Match them correctly.
Q
P
O
R
100°
Column–I Column–II
(A)OPR (p) Cannot be calculated
(B) POR (q) 10°
(C) QPR (r) 200°
(D) ORP (s) 160°
(A) (A-s), (B-r), (C-q), (D-p) (B) (A-q), (B-r), (C-s), (D-p)
(C) (A-p), (B-q), (C-r), (D-s) (D) (A – q), (B – r, s), (C – p), (D – q)
INTEGER ANSWER TYPE QUESTIONS
The answer to each of the questions is a single-digit integer, ranging from 0 to 9.
26. The length of a chord which is at a distance 6 cm from the center of circle of radius 10 cm is 4k,
then k is ______.
27. A chord of length 24 cm is draw in a circle of radius is 13 cm and then the distance of chord from the
center is ____.
28. The number of circle passing through three collinear points are ______.

#Class 9 #MCQ #Chapter_10 #Circles

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