Class 9 Practice – Level 3 – Set 2 – Circles

Total questions: 15

In the given figure, I is the incentre of △ABC. AI produced meets the circumcircle of △ABC at D;∠ABC=55° and ∠ACB=65°.Find (i) ∠BCD (ii) ∠CBD (iii) ∠DCI (iv) ∠BIC.

Topic: Incenter and Circumcircle in a Triangle

∠CBD=90°, ∠DCI=30°, ∠BIC=92.5°, ∠BCD120°

∠DCI=80°, ∠BIC=90°, ∠CBD=62.5°, ∠BCD=120°

∠BCD=30°, ∠CBD=30°,∠DCI=62.5°, ∠BIC=120°

None of these

None

In the given figure, AB is a diameter of the circle with centre O, AC and BD produced meet at E and ∠COD=40°. Calculate ∠CED.

Topic: Angles in a Circle

∠CED = 50°

∠CED = 70°

∠CED = 60°

∠CED = 90°

None

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

Topic: Chords and Their Properties in Circles

OAC = ∠OAB

OCB = ∠OBC

OAB = ∠OAC

AOB = ∠BAO

None

In the given figure, if ∠ABC = 20° , then ∠AOC is equal to

Topic: Angles in a Circle

20°

80°

50°

40°

None

A chord of length 30 cm is drawn in a circle of radius 17 cm. Find its distance from the centre off the circle.

Topic: Chords and Their Properties in Circles

6 cm

5 cm

7 cm

8 cm

None

In the given figure, O is the centre of the circle and ∠AOC=160°. Find 3 ∠𝑦 − 2 ∠𝑥.

Topic: Central Angles

120°

110°

170°

140°

None

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 Quadrilateral Angles

108°

88°

115°

72°

None

If chords of congruent circles subtend equal angles at their centres, then which of the following statement is correct?

Topic: Congruence of Circles

AB = CD

AC = BD

CB = CA

None of these

None

In the given figure, if ∠DAB = 60º, ∠ABD = 50º, then ∠ACB is equal to:

Topic: Angles in a Circle

70°

50°

60°

80°

None

10.

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: Chords and Their Properties in Circles

8 cm

9 cm

10 cm

15 cm

None

11.

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

Topic: Angles in a Circle

120°

80°

100°

110°

None

12.

If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is :

Topic: Circle and Triangle Properties

50 cm

20 cm

10 cm

None of the above

None

13.

In the figure, ∠BAD=70°,∠ABD=56° and ∠ADC=72°. Calculate (i) ∠BDC (ii) ∠BCD (iii) ∠CBD.

Topic: Angles in a Cyclic Quadrilateral

∠BCD=18°, ∠BCA=110°, ∠BCD=55°

∠BDC=18°, ∠BCD=110°, ∠CBD= 52°

∠CDB=52°,∠CDB= 62°, ∠CBD= 52°

None of these

None

14.

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 from the Centre to a Chord

3.4 cm

3.6 cm

1.4 cm

1.8 cm

None

15.

If the perpendicular bisector of a chord AB of a circle PXAQBY intersect the circle at P and Q, prove that arc PXA ≅ arc PYB.

Topic: Chords and Their Properties in Circles

Arc PXA ≅ Arc PYB

Arc NXA ≅ Arc MYB

Arc BXA ≅ Arc YPB

None of these

None

1 out of 15

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Class 9 Practice – Level 3 – Set 2 – Circles

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