Questions & Answers: "Circles"

Complete guide to "Circles" for Math students. Below you will find important questions and model answers to help you prepare.

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12 Questions
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1.

In following figure, two congruent circles have centres O and O′. Arc AXB subtends an angle of 75° at the centre O and arc A′ Y B′ subtends an angle of 25° at the centre O′. Then the ratio of arcs A X B and A′ Y B′ is

Question Diagram

Options

❌

2:1

❌

1:2

✅

3:1

❌

1:3

2.

In following figure, AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD, respectively. If ∠POQ = 150°, then ∠APQ is equal to

Question Diagram

Options

❌

30°

✅

75°

❌

15°

❌

60°

3.

AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is

Options

❌

17 cm

❌

15 cm

❌

4 cm

✅

8 cm

4.

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

Question Diagram

Options

✅

2 cm

❌

3 cm

❌

4 cm

❌

5 cm

5.

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:

Options

❌

6 cm

❌

8 cm

✅

10 cm

❌

12 cm

6.

In following figure, if ∠ABC = 20º, then ∠AOC is equal to:

Question Diagram

Options

❌

20°

✅

40°

❌

60°

❌

10°

7.

In following figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to:

Question Diagram

Options

❌

30°

❌

60°

❌

90°

✅

45°

8.

In following figure, if ∠OAB = 40º, then ∠ACB is equal to:

Question Diagram

Options

✅

50°

❌

40°

❌

60°

❌

70°

9.

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

Question Diagram

Options

❌

60°

❌

50°

✅

70°

❌

80°

10.

ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140º, then ∠BAC is equal to:

Options

❌

80°

✅

50°

❌

40°

❌

30°

11.

In following figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to:

Question Diagram

Options

❌

30°

❌

45°

✅

60°

❌

120°

12.

In following figure, ∠AOB = 90º and ∠ABC = 30º, then ∠CAO is equal to:

Question Diagram

Options

❌

30°

❌

45°

❌

90°

✅

60°