Class 10 Practice – Level 2 – Set 1 - Circles

Total questions: 25

In the given figure, AB is the diameter of a circle with centre O and AT is a tangent. If ∠AOQ = 58°, find ∠ATQ.

Topic: Angles in a Circle

61°

60°

80°

70°

None

An isosceles triangle ABC, with AB = AC, circumscribes a circle. the point of contact P bisects the base BC. Is it true or not?

Topic: Properties of Isosceles Triangle and Circle

True

False

Cannot be predicted

More information needed

None

The circumference of a circle exceeds its diameter by 45 cm. What is the circumference of the circle?

Topic: Circumference of a Circle

46 cm

28 cm

34 cm

66 cm

None

The circumference of a circle is 39.6 cm. What should be value of the area?

Topic: Area of a Circle

145.36 sq.cm

254.69 sq.cm

45.12 sq.cm

124.74 sq.cm

None

What is the radius of a circle whose perimeter and area are numerically equal?

Topic: Radius of a Circle

5 cm

2 cm

8 cm

6 cm

None

What is the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4 cm and 3 cm?

Topic: Diameter of a Circle

20 cm

35 cm

70 cm

10 cm

None

The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Topic: Radius of a Circle

60 cm

40 cm

20 cm

10 cm

None

What is the perimeter of a semicircular protractor whose diameter is 14 cm?

Topic: Perimeter of a Semicircle

88 cm

22 cm

36 cm

11 cm

None

A sheet of paper is in the from of rectangular ABCD in which AB = 40 cm and AD = 28 cm. A semi-circular portion with BC as diameter is cut off. What should be the area of the remaining paper.

Topic: Area of Remaining Shape

$ \displaystyle \text{812 c}{{\text{m}}^{2}}$

$ \displaystyle \text{745 c}{{\text{m}}^{2}}$

$ \displaystyle \text{685 c}{{\text{m}}^{2}}$

$ \displaystyle \text{552 c}{{\text{m}}^{2}}$

None

10.

What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm?

Topic: Diameter of a Circle

66 cm

55 cm

12 cm

26 cm

None

11.

What is the area of a circle whose circumference is 8π?

Topic: Area of a Circle

24 π

16 π

30π

14 π

None

12.

In the given figure, a circle touches all four sides of a quadrilateral ABCD with AB = 6 cm, BC=7 cm and CD = 4 cm. Find AD

Topic: Tangents and Quadrilateral Properties

3 cm

2 cm

4 cm

5 cm

None

13.

If a chord AB subtends an angle of 60° at the centre of a circle, then angle between the tangents at A and B will be:

Topic: Angle Between Tangents

60°

90°

30°

120°

None

14.

The tangent to the circumcircle of an isosceles △ABC at A, in which AB = AC, then:

Topic: Tangents to Circumcircle

Tangent will be parallel to BC

Tangent will not be parallel to BC

Tangent will be equal to BC

Tangent will not be equal to BC

None

15.

Two tangents PQ and PR are drawn from an external point to a circle with center O. The QORP will be:

Topic: Tangent to a Circle

Cyclic quadrilateral

Quadrilateral

Rhombus

Parallelogram

None

16.

The center of a circle touching two intersecting lines lies on the angle bisector of the lines. Is it true or not?

Topic: Circle and Angle Bisector

True

False

Cannot be determined

More information required

None

17.

In the given figure, AB and CD are common tangents to two circles of unequal radii. What can you say about AB and CD?

Topic: Common Tangents to Two Circles

AB is equal to CD

AB is not equaL to CD

AB is parallel to CD

None of the above

None

18.

In the given figure, If the common tangents AB and CD to two circles intersect at E. Then what can be inferred about AB and CD?

Topic: Intersection of Common Tangents

AB is equal to CD

AB is not equal to CD

AB is parallel to CD

None of the above

None

19.

A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Then R bisects the arc PRQ. Is it true or not?

Topic: Chord and Parallel Tangent

True

False

Cannot be determined

Incomplete information

None

20.

The tangents drawn at the ends of a chord of a circle does not make equal angles with the chord.

Topic: Tangents and Angles with Chord

True

False

Cannot be determined

Incomplete information

None

21.

From an external point P, two tangents, PA and PB are drawn to a circle with centre 0 . At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.

Topic: Perimeter of Tangent Triangle

50 cm

20 cm

70 cm

45 cm

None

22.

If angle between two radii of a circle is 130°, the angle between the tangents at the ends of the radii is :

Topic: Tangent and Radius

90°

50°

70°

40°

None

23.

In the given figure, the pair of tangents AP and AQ drawn from an external point A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. Then the radius of the circle is:

Topic: Length of Tangents