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Test: Circles- 1 - Class 9 MCQ

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25 Questions MCQ Test Mathematics (Maths) Class 9 - Test: Circles- 1

Test: Circles- 1 for Class 9 2024 is part of Mathematics (Maths) Class 9 preparation. The Test: Circles- 1 questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Circles- 1 MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Circles- 1 below.

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Test: Circles- 1 - Question 1

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In the given figure, ∠BPC = 19^o, arc AB = arc BC = arc CD. Then, the measure of ∠APD is

A.
59^o
B.
57^o
C.
76^o
D.
38^o

Test: Circles- 1 - Question 2

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ABCD is a parallelogram. A circle passes through A and D and cuts AB at E and DC at F. If ∠BEF = 80^o, then ∠ABC is equal to

A.
120^o
B.
100^o
C.
80^o
D.
75^o

Detailed Solution for Test: Circles- 1 - Question 2

Given, ABCD is a parallelogram and AEFD is a cyclic quadrilateral.
∠BEF=80^∘
Now, ∠ADC=∠BEF=80^∘ (Angle of a cyclic quadrilateral is equal to the opposite exterior angle )
Also, now in parallelogram ABCD,
∠ABC=∠ADC=80^∘ (Opposite angles of a parallelogram are equal)

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Test: Circles- 1 - Question 3

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In the given figure, ABCD is a quadrilateral inscribed in circle with centre O. CD is produced to E. If ∠ADE = 95^o and ∠OBA = 30^o, then ∠OAC is equal to

A.
20^o
B.
15^o
C.
10^o
D.
5^o

Detailed Solution for Test: Circles- 1 - Question 3

Test: Circles- 1 - Question 4

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In a figure, O is the centre of the circle with AB as diameter. If ∠AOC = 40^o, the value of x is equal to

A.
80^o
B.
70^o
C.
50^o
D.
60^o

Detailed Solution for Test: Circles- 1 - Question 4

The value of x is equal to 70°.

Since AB is the diameter, angle AOC is a central angle and its value is twice the inscribed angle subtended by the same chord. Therefore, x = 2 * 35° = 70°.

Test: Circles- 1 - Question 5

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The given figures show two congruent circles with centre O and O’. Arc AXB subtends an angle of 75^o at the centre and arc A’YB’ subtends an angle of 25^o at the centre O’. Then, the ratio of arcs AXB to A ‘YB’ is

A.
it is 3 : 1
B.
it is 1 : 3
C.
it is 1 : 2
D.
it is 2 : 1

Detailed Solution for Test: Circles- 1 - Question 5

Because the circles are congruent, therefore their radius are same

Length of arc AXB = [θ/(360°)] × 2πr = [(75°)/(360°)] × 2πr

Length of arc A’YB’ = [θ/(360°)] × 2πr = [(25°)/(360°)] × 2πr

Required Ratio = ([(75°)/(360°)] × 2πr) : ([(25°)/(360°)] × 2πr) = 3 : 1

Test: Circles- 1 - Question 6

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If a chord of a circle is equal to its radius, then the angle subtended by this chord in major segment is

A.
45^o
B.
30^o
C.
60^o
D.
90^o

Test: Circles- 1 - Question 7

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The given figure shows two intersecting circles. If ∠ABC = 75^o, then the measure of ∠PAD is

A.
75^o
B.
125^o
C.
105^o
D.
150^o

Test: Circles- 1 - Question 8

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In the given figure, ABCD is a cyclic quadrilateral in which ∠BAD = 75^o, ∠ABD = 58^o and ∠ADC = 77^o , AC and BD intersect at P. the measure of ∠DPC is

A.
92^o
B.
105^o
C.
90^o
D.
94^o

Detailed Solution for Test: Circles- 1 - Question 8

∠DBA = ∠DCA = 58° …(1)

[Angles in same segment] ABCD is a cyclic quadrilateral :

Sum of opposite angles = 180 degrees

∠A +∠C = 180°

75° + ∠C = 180°

∠C = 105°

Again,

∠ACB + ∠ACD = 105°

∠ACB + 58° = 105°

or ∠ACB = 47° …(2)

Now, ∠ACB = ∠ADB = 47° [Angles in same segment]

Also, ∠D = 77° (Given)

Again From figure, ∠BDC + ∠ADB = 77°

∠BDC + 47° = 77°

∠BDC = 30°

In triangle DPC

∠PDC + ∠DCP + ∠DPC = 180°

30° + 58° + ∠DPC = 180°

or ∠DPC = 92°

Test: Circles- 1 - Question 9

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For what value of x in the figure, points A, B, C and D are concyclic ?

A.
9^o
B.
12^o
C.
11^o
D.
10^o

Test: Circles- 1 - Question 10

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Greatest chord of a circle is called its

A.
chord
B.
secant
C.
radius
D.
diameter

Test: Circles- 1 - Question 11

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In the given figure PQ and RS are two equal chords of a circle with centre O. OA and OB are perpendiculars on chords PQ and RS, respectively. If ∠AOB = 140^o, then ∠PAB is equal to

A.
40^o
B.
70^o
C.
60^o
D.
50^o

Test: Circles- 1 - Question 12

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In the given figure, chords AB and CD intersect at P. If ∠DPB = 88^o and ∠DAP = 46^o, then the measure of ∠ABC is

A.
48^o
B.
44^o
C.
42^o
D.
46^o

Test: Circles- 1 - Question 13

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AD is diameter of a circle and AB is a chord. If AD = 50 cm, AB = 48 cm, then the distance of AB from the centre of the circle is

A.
6 cm
B.
8 cm
C.
5 cm
D.
7 cm

Test: Circles- 1 - Question 14

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In the given figure, O is the centre of the circle. If ∠CAB = 40^o and ∠CBA = 110^o, the value of x is :

A.
80^o
B.
55^o
C.
60^o
D.
50^o

Test: Circles- 1 - Question 15

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Angle formed in minor segment of a circle is

A.
a straight angle
B.
an acute angle
C.
a right angle
D.
an obtuse angle

Test: Circles- 1 - Question 16

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In the given figure PQ = QR = RS and ∠PTS = 75^o then the measure of ∠QOR is

A.
25^o
B.
20^o
C.
50^o
D.
75^o

Test: Circles- 1 - Question 17

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In the given figure, O is the centre of the circle ABE is a straight line,. If ∠DBE = 95^o then ∠AOD is equal to

A.
190^o
B.
170^o
C.
180^o
D.
175^o

Test: Circles- 1 - Question 18

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The given figure shows two congruent circles with centre O and O’ intersecting at A and B. If ∠AO′B = 50^o, then the measure of ∠APB is

A.
45^o
B.
25^o
C.
40^o
D.
50^o

Test: Circles- 1 - Question 19

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Angle inscribed in a semicircle is :

A.
60^o
B.
90^o
C.
75^o
D.
120^o

Detailed Solution for Test: Circles- 1 - Question 19

Test: Circles- 1 - Question 20

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

A.
3
B.
1
C.
2
D.
0

Test: Circles- 1 - Question 21

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In the given figure, if ∠ABC = 50^o and ∠BDC = 40^o, then ∠BCA is equal to

A.
90^o
B.
50^o
C.
100^o
D.
40^o

Test: Circles- 1 - Question 22

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In the given figure, chords AB and CD intersect each other at right angles. Then, ∠x+∠y is equal to

A.
75^o
B.
90^o
C.
45^o
D.
60^o

Test: Circles- 1 - Question 23

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In the given figure if ∠CAB = 49^o and ∠ADC = 43^o, then the measure of ∠ACB is

A.
92^o
B.
88o
C.
74^o
D.
96^o

Test: Circles- 1 - Question 24

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In the given figure, O is the centre of the circle. If ∠QPR is 50^o, then ∠QOR is :

A.
130^o
B.
50^o
C.
100^o
D.
40^o

Test: Circles- 1 - Question 25

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If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to

A.
60°
B.
70°
C.
80°
D.
90°

Detailed Solution for Test: Circles- 1 - Question 25

As per the given question:

We can see, OP is the radius of the circle to the tangent PT and OQ is the radius to the tangents TQ.

So, OP ⊥ PT and TQ ⊥ OQ

∴ ∠OPT = ∠OQT = 90°

Now, in the quadrilateral POQT, we know that the sum of the interior angles is 360°

So, ∠PTQ + ∠POQ + ∠OPT + ∠OQT = 360°

Now, by putting the respective values, we get,

⇒ ∠PTQ + 90° + 110° + 90° = 360°

⇒ ∠PTQ = 70°

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Important Questions for Circles- 1

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Circles- 1 MCQs with Answers

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Test: Circles- 1 - Class 9 MCQ

25 Questions MCQ Test Mathematics (Maths) Class 9 - Test: Circles- 1

In the given figure, ∠BPC = 19o, arc AB = arc BC = arc CD. Then, the measure of ∠APD is

ABCD is a parallelogram. A circle passes through A and D and cuts AB at E and DC at F. If ∠BEF = 80o, then ∠ABC is equal to

In the given figure, ABCD is a quadrilateral inscribed in circle with centre O. CD is produced to E. If ∠ADE = 95o and ∠OBA = 30o, then ∠OAC is equal to

Mathematics (Maths) Class 9

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Important Questions for Circles- 1

Circles- 1 MCQs with Answers

Online Tests for Circles- 1 Mathematics (Maths) Class 9

In the given figure, ∠BPC = 19^o, arc AB = arc BC = arc CD. Then, the measure of ∠APD is

ABCD is a parallelogram. A circle passes through A and D and cuts AB at E and DC at F. If ∠BEF = 80^o, then ∠ABC is equal to

In the given figure, ABCD is a quadrilateral inscribed in circle with centre O. CD is produced to E. If ∠ADE = 95^o and ∠OBA = 30^o, then ∠OAC is equal to