Class 9 Practice – Level 2 - Set 2 – Circles

Total questions: 25

In the given figure, ΔABC is an equilateral triangle and ABDC is a cyclic quadrilateral, then find the measure of ∠BDC.

Topic: Cyclic Quadrilateral Angles

∠BDC = 120°

∠BDC = 130°

∠BDC = 140°

None of these

None

If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

Topic: Isosceles Trapezium and Cyclic Properties

ABCD is a cyclic triangle.

ABCD is a cyclic square.

ABCD is a cyclic quadrilateral.

All of these

None

In the figure, POQ is a diameter and PQRS is a cyclic quadrilateral. If ∠PSR=150°, find ∠RPQ.

Topic: Cyclic Quadrilateral Angles

40°

60°

80°

90°

None

If the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent, then select the correct option?

Topic: Perpendicular Bisectors and Cyclic Quadrilaterals

AB,BC,CD and BA pass through the centre O are concurrent

AB,BC,CD and BG pass through the centre O are concurrent

AB,BC,CD and DA pass through the centre O are concurrent

All of these

None

In a cyclic quadrilateral ABCD, if (∠B−∠D)=60°, then the smaller of the two angles is...

Topic: Cyclic Quadrilateral Angles

60°

70°

90°

110°

None

In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to ___.

Topic: Geometry of Circles and Perpendiculars

7 cm

9 cm

2 cm

8 cm

None

In the adjoining figure, ABCD is a cyclic quadrilateral in which ∠BCD=100° and ∠ABD=50°. Find ∠ADB.

Topic: Angles in a Cyclic Quadrilateral

80°

60°

70°

50°

None

If ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC=55° and ∠BAC=45°, find ∠BCD.

Topic: Cyclic Quadrilateral Angles

50°

60°

80°

70°

None

Two circles intersect at two points A and B. AD and AC are diameters to the two circles, then ∠DBC is...

Topic: Intersecting Circles and Angles

150°

180°

140°

120°

None

10.

In the given figure, ∠ABC=69° and ∠ACB=31°. Find ∠BDC.

Topic: Angles in a Circle

80°

70°

50°

60°

None

11.

In the figure, ∠BAD=70°,∠ABD=56° and ∠ADC=72°. Calculate ∠BCD .

Topic: Cyclic Quadrilateral Angles

∠BDC=110°

∠BCD=120°

∠CDB=70°

∠DBC= 60°

None

12.

In the given figure, O is the centre of the circle. If ∠PBC=25° and ∠APB=110°, find the value of ∠ADB.

Topic: Angles in a Circle

55°

65°

75°

85°

None

13.

In the figure, given below, AOB is a diameter of the circle and ∠AOC=110°. Find ∠BDC.

Topic: Angles in a Circle

35°

40°

60°

75°

None

14.

In the given figure, O is the centre of a circle, ∠AOB=40° and ∠BDC=100°, find ∠OBC.

Topic: Angle at the Centre

40°

50°

90°

60°

None

15.

In the given figure, O is the centre of the circle and ∠OBC=50°. Calculate

Topic: Central Angles

(i) $∠ ADC$
(ii) $∠ AOC$

(i) ∠ADC=130° (ii) ∠AOC=100°

(i) ∠ADC=110° (ii) ∠AOC=100°

(i) ∠ADC=130° (ii) ∠AOC=110°

(i) ∠ADC=120° (ii) ∠AOC=100°

None

16.

In the figure, the diameter CD of a circle with centre O is perpendicular to the chord AB. If AB=12 cm and CE=3 cm, find the radius of the circle.

Topic: Perpendicular Chord and Radius of a Circle

6.5 cm

7.5 cm

5.5 cm

7.2 cm

None

17.

The adjoining figure shows a circle with centre O in which a diameter AB bisects the chord PQ at point R. If PR=RQ=8 cm and RB=4 cm, find the radius of the circle

Topic: Bisected Chord and Radius of Circle

30 cm

20 cm

10 cm

15 cm

None

18.

O is the centre of the circle. AB and CD are two chords of the circle. OM⊥AB and ON⊥CD. If OM=ON=2 cm and AM=BM=4.5 cm, then CD is equal to

Topic: Perpendicular Chords and Angles

8 cm

9 cm

10 cm

None of these

None

19.

O is the centre of the circle having radius 5 cm. AB and AC are two chords such that AB=AC=6 cm. If OA meets BC at M, then OM is equal to

Topic: Perpendicular Chords and Angles

1.4 cm

3.4 cm

3.6 cm

1.8 cm

None

20.

In the given figure, AB∣∣DC and ∠BAD=100°. Calculate ∠ABC.

Topic: Parallel Lines and Angles

100°

80°

150°

120°

None

21.

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

Topic: Parallel Lines and Transversals

75°

55°

45°

65°

None

22.

ABCD is a cyclic quadrilateral AE is drawn parallel to CD and BA is produced. If ∠ABC=92° and ∠FAE=20°, then ∠BCD=

Topic: Cyclic Quadrilaterals and Parallel Lines

88°

75°

115°

108°

None

23.

Chords AB and CD of a circle are produced to meet at the point P, outside the circle, and AD is the diameter of the circle. If ∠DAP=36° and ∠APC=30°, then what will be the measure of ∠CBD ?

Topic: Angle Between Chords and Tangents

24°

26°

16°

12°

None

24.

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 respectivelyIn 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

50° and 25°

40° and 25°

50° and 35°

60° and 75°

None

25.

In the given figure, O is the centre of the circle. If ∠ADC=140°, find x.

Topic: Angles in a Circle

35°

40°

50°

45°

None

1 out of 25

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Class 9 Practice – Level 2 - Set 2 – Circles

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