Class 9 Practice – Level 1 – Circles

Total questions: 40

In the given figure two circles are congruent if they have the same radii. select the correct option?

Topic: Congruence of Circles

∠AOB = ∠CO′D

∠ABO = ∠CO′D

∠AOB = ∠OC′D

None of these

None

If chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Topic: Chords and Angles in Congruent Circles

True

False

None

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

Topic: Common Chord Length

3cm

6cm

8cm

None of these

None

If two equal chords of a circle intersect within the circle, within the circle in the given figure, which of the following option is true ?

Topic: Intersecting Chords

EA = EC and AE = EA

EB = EC and AE = ED

ED = EC and AE = PD

None of these

None

If two equal chords of a circle intersect within the circle, which option is correct in the given figure?

Topic: Intersecting Chords

∠OXA= ∠OXD

∠OXA = ∠CXD

∠ONA = ∠OXD

None of these

None

If a line intersects two concentric circles (circles with the same centre) with centre O at A,B,C and D, select the correct option?

Topic: Concentric Circles

AD=BC

CB=AC

AB=CD

All of these

None

In the figure A,B and C are three points on a circle with centre O such that ∠BOC=30° and ∠AOB=60°. If D is a point on the circle other than the arc ABC, find ∠ADC.

Topic: Angles in a Circle

45°

90°

35°

65°

None

A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

Topic: Angle Subtended by a Chord

200°, 60°

250° , 40°

150° , 30°

None of these

None

In the figure, angle PQR=100°, where P,Q and R are points on a circle with centre O. Find angle OPR.

Topic: Angles in a Cyclic Quadrilateral

10°

20°

30°

40°

None

10.

In the figure, ∠ABC=69°, ∠ACB=31°, find ∠ADC.

Topic: Angles in a Circle

50°

60°

100°

111°

None

11.

In the given figure, A,B,C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC=130° and ∠ECD=20°. Find ∠BAC.

Topic: Intersecting Chords and Angles

50°

90°

110°

65°

None

12.

In the given figure, AB is parallel to DC,∠BCE=80° and ∠BAC=25° . Find ∠CAD

Topic: Parallel Chords and Angles

55°

65°

25°

75°

None

13.

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ΔDBC=70°, ΔBAC is 30°, find ∠ BCD. Further if AB=BC, find ∠ ECD.

Topic: Cyclic Quadrilateral Angles

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC = 30° find ∠BCD. Further if AB = BC, find ∠ECD.

∠ BCD = 80°, ∠ ECD = 50°

∠ BCD = 90°, ∠ ECD = 60°

∠ BCD = 50°, ∠ ECD = 70°

∠ BCD = 75°, ∠ ECD = 75°

None

14.

If the non-parallel sides of a trapezium are equal, what is ∠A + ∠C.

Topic: Angles in an Isosceles Trapezium

180°

90°

60°

40°

None

15.

Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A,D and P,Q respectively (see figure) and select the correct option?

Topic: Intersecting Chords and Angles

∠AQP = ∠QCD

∠ACP = ∠QCD

∠ADP = ∠QCP

None of these

None

16.

If circles are drawn taking two sides of a triangle as diameters, select the correct option?

Topic: Circles on Triangle's Sides as Diameters

C lies on the BC.

D lies on the BC.

D lies on the AC.

None of above

None

17.

ABC and ADC are two right triangles with common hypotenuse AC. select the correct answer?

Topic: Right Triangles with Common Hypotenuse

∠CBD=∠CAD

∠CAD=∠CBD

∠ACD=∠CBD

None of the above

None

18.

ABCD is a cyclic parallelogram which is the following statement is correct?

Topic: Cyclic Parallelogram Properties

ABCD is a triangle

ABCD is a Circle.

ABCD is a rectangle.

None of these

None

19.

In the given figure the line of centres of two intersecting circles subtends equal angles at the two points of intersection, choose the correct option?

Topic: Line of Centres and Intersection Angles

∠ADB=∠ACB

∠ACB=∠ADB

∠ABD=∠ADB

None of these

None

20.

In the figure, ∠ABC=69°, ∠ACB=31°, find ∠BDC.

Topic: Angles in a Cyclic Quadrilateral

60°

70°

80°

50°

None

21.

Two chords A B and C D of lengths 5 cm and 11 ~cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between A B and C D is 6 , find the radius of the circle.

Topic: Parallel Chords and Radius

5.6 cm

8.6 cm

6.6 cm

5.8 cm

None

22.

The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?

Topic: Parallel Chords and Radius

10 cm

8 cm

6 cm

3 cm

None

23.

If the circle drawn with any side of a rhombus as diameter, passes through the, point of intersection of its diagonals.

Topic: Circle and Rhombus Properties

Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals.

True

False

None

24.

ABCD is a parallelogram. The circle through A,B and C intersect CD (produced if necessary) at E, select the correct option?

Topic: Circle and Parallelogram Properties

AC=DE

AD=DE

AB=DE

None of these

None

25.

A C and B D are chords of a circle which bisect each other. find the value of ∠A ?

Topic: Perpendicular Chords and Angles

90°

50°

60°

80°

None

26.

If a line intersects two concentric circles (circles with the same centre) with centre O at A,B,C and D, choose the correct option ?

Topic: Concentric Circles

BO = CD

BC = AD

AB = CD

None of these

None

27.

In the figure, O is the centre of the circle. If ∠BOD=160°, find the values of x and y.

Topic: Central Angle and Arcs

x = 120°, y = 140

x = 80, y = 100°

x = 40°, y = 80°

None of these

None

28.

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, what is the value of each internal angle?

Topic: Cyclic Quadrilateral Angles

60°

40°

90°

50°

None

29.

In the given figure, the straight lines AB and CD pass through the centre O of the circle. If ∠AOD=75 ∘ and ∠OCE=40 ∘ , Then (i) ∠CDE (ii) ∠OBE are respectively

Topic: Angles in a Circle

75° and 55°

50° and 25°

40° and 55°

45° and 75°

None

30.

In the adjoining figure, two circles with centres A and B, and of radii 5 cm and 3 cm touch each other internally. If the perpendicular bisector of AB meets the bigger circle in P and Q, find the length of PQ.

Topic: Internal Tangents and Circle Properties

$\displaystyle 6\sqrt{6}cm$

$\displaystyle 4\sqrt{6}cm$

$\displaystyle 4\sqrt{8}cm$

$\displaystyle 4\sqrt{4}cm$

None

31.

Given an arc of a circle, complete the circle.

Topic: Central Angle and Arcs

Taking the centre and the Diameter so obtained

Taking the centre and the radius so obtained,

Taking the mid-point and the radius so obtained,

None of these

None

32.

In the given figure, ∠ABD=54° and ∠BCD=36°, calculate ∠ACD.

Topic: Angles in a Circle

45°

65°

54°

47°

None

33.

O is the centre of the circle, If chord AD= chord CD, then x = ?

Topic: Equal Chords and Angles

70°

50°

35°

45°

None

34.

In the adjoining figure, DE is a chord parallel to diameter AC of the circle with centre O. If ∠CBD=60°,calculate ∠CDE.

Topic: Parallel Chords and Angles

70°

40°

30°

25°

None

35.

In the adjoining figure, AB and AC are two equal chords of a circle with centre O, which of the following option is correct?

Topic: Equal Chords in a Circle

∠OAB = ∠OAC

∠OCB = ∠OCA

∠OAC = ∠OAB

None of these

None

36.

If a diameter of a circle bisects each of the two chords of a circle then which is the following answer is correct ?

Topic: Diameter and Bisected Chords

AB∥CA

AB∥CD

AB∥CB

All of these

None

37.

Two equal circles intersect in P and Q. A straight line through P meets the circles in A and B, select the correct option?

Topic: Intersecting Circles and Chords

QA=AB

QB=AQ

QB=AD

None of these

None

38.

In the adjoining figure BC is a diameter of a circle with centre O. If AB and CD are two chords such that AB∥CD, select the correct option?

Topic: Parallel Chords and Diameter

AB = CD

OD = BD

OM = CL

None of these

None

39.

The two different circles cannot intersect each other at more than two points ?

Topic: Intersection of Two Circles

True

False

None

40.

If the diameter of a circle perpendicular to one of the two parallel chords of a circle is perpendicular to the other and bisects it. then which of the following statement is correct?

Topic: Perpendicular Diameter and Parallel Chords

NC=ND

ON=AD

CB=NN

All of these

None

1 out of 40

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Class 9 Practice – Level 1 – Circles

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