Class 10 Quiz Level 1 (Easy) – Circles

Total questions: 30

How many tangents can a circle have?

Topic: Number of Tangents to a Circle

Deselect Answer

Fifty tangents

Hundred tangents

Infinite tangents

No tangents

None

PQ and PT are tangents to a circle with centre O and radius 5 cm. If PQ =12 cm, then the perimeter of the quadrilateral PQOT is:

Topic: Perimeter of a Quadrilateral with Tangents

Deselect Answer

30 cm

34 cm

36 cm

40 cm

None

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

Topic: Angle Between Diameter and Tangent

Deselect Answer

90°

61°

82°

72°

None

In the given figure ,O is the centre of a circle. PT and PQ are tangents to the circle from an external point P. If ∠TPQ = 70°, find ∠TRQ.

Topic: Angle Between Two Tangents from an External Point

Deselect Answer

90°

55°

67°

70°

None

Find the perimeter of the shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircle.

Topic: Perimeter of Shaded Region

Deselect Answer

25cm

56cm

33cm

72 cm

None

In the given figure, two circles touch each other at C and AB is a tangent to both circles. ∠ACB equal to :

Topic: Tangents to Two Circles

Deselect Answer

60°

45°

120°

90°

None

The tangent at any point of a circle is

Topic: Tangent to a Circle

Deselect Answer

Perpendicular to the radius through the point of contact

Parallel to the radius through the point of contact

Supplementary to the radius through the point of contact

None

The angle between two tangents to a circle may be 0°. Is it true or not?

Topic: Angle Between Two Tangents

Deselect Answer

True

False

Cannot be determined

Sometimes true

None

The length PB = _________ cm.

Topic: Length of a Chord

Deselect Answer

None

10.

A tangent intersects the circle at:

Topic: Point of Contact of a Tangent

Deselect Answer

Many points

Two distinct points

One point

None of the above

None

11.

In the adjoining figure, OACB is a quadrant of a circle of radius 7 cm. The perimeter of the quadrant is [Take π = $ \displaystyle \dfrac{22}{7}$] ?

Topic: Perimeter of a Quadrant

Deselect Answer

25 cm

30 cm

45 cm

50 cm

None

12.

If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is:

Topic: Chord Length in Concentric Circles

Deselect Answer

3 cm

6 cm

9 cm

1 cm

None

13.

In the given figure, are two concentric circles of radii 6 cm and 4 cm with centre O. If AP is a tangent to the larger circle and BP to the smaller circle and length of AP is 8 cm, find the length of BP.

Topic: Tangents to Concentric Circles

Deselect Answer

$\displaystyle \sqrt{{116}}\text{ }cm$

$\displaystyle 10\text{ cm}$

$\displaystyle 2\sqrt{{21}}\text{ cm}$

$\displaystyle 2\sqrt{{12}}\text{ cm}$

None

14.

Two concentric circles of radii a and b (a > b) are given. What is the length of the chord of the larger circle which touches the smaller circle.

Topic: Chord Touching Smaller Circle

Deselect Answer

$\displaystyle \sqrt{{{{a}^{2}}-{{b}^{2}}}}$

$\displaystyle 2\sqrt{{{{a}^{2}}-{{b}^{2}}}}$

$\displaystyle \sqrt{{{{a}^{2}}+{{b}^{2}}}}$

$\displaystyle 2\sqrt{{{{a}^{2}}+{{b}^{2}}}}$

None

15.

In the given figure, if AB = AC, then which of the following option is correct?

Topic: Properties of Chords in a Circle

Deselect Answer

BE = EC

DF = BC

DB = FC

EC = DF

None

16.

The lengths of two tangents drawn from an external point to a circle are equal.

Topic: Length of Tangents from an External Point

Deselect Answer

True

False

More information is required

Cannot be predicted

None

17.

The length of tangent from an external point P on a circle is always greater than the radius of the circle.

Topic: Tangent Length vs. Radius

Deselect Answer

True

False

More information is required

None of the above

None

18.

The parallelogram circumscribing a circle will be a:

Topic: Circumscribing Parallelogram Properties

Deselect Answer

Rhombus

Rectangle

Square

Trapezium

None

19.

PQ is a tangent drawn from an external point P to a circle with centre O, QOR is the diameter of the circle. If ∠POR = 120°, what is the measure of ∠OPQ ?

Topic: Tangent and Radiu

Deselect Answer

55°

90°

30°

70°

None

20.

In the given figure, PA and PB are tangents to a circle from an external point P such that PA=4 cm and ∠BAC = 135°. Find the length of chord AB.

Topic: Tangents and Chords in a Circle

Deselect Answer

$ \displaystyle 2\sqrt{4}$ cm

$ \displaystyle 6\sqrt{4}$ cm

$ \displaystyle 4\sqrt{2}$ cm

$ \displaystyle 5\sqrt{2}$ cm

None

21.

In the given figure, if ∠AOD = 135°, then ∠BOC is equal to

Topic: Angle Between Chord and Tangent

Deselect Answer

52.5°

45°

62.5°

25°

None

22.

How many parallel tangents a circle can have at a single time?

Topic: Parallel Tangents of a Circle

Deselect Answer

Only one

Two

Four

Infinite

None

23.

In the given figure, on a circle of radius 7 cm, tangent PT is drawn from a point P such that PT=24 cm. If O is the center of the circle, then the length of PR is

Topic: Tangent and Radius

Deselect Answer

30 cm

28 cm

32 cm

25 cm

None

24.

How many tangents can a circle have?

Topic: Number of Tangents to a Circle

Deselect Answer

Fifty tangents

Hundred tangents

Infinite tangents

No tangents

None

25.

The two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

Topic: Chord Properties in Concentric Circles

Deselect Answer

True

False

Cannot be predicted

More information required

None

26.

In the given figure, AB is a chord of a circle, with centre O, such that AB = 16 cm and radius of circle is 10 cm. Tangents at A and B intersect each other at P. Find the length of PA.

Topic: Tangents and Chords in a Circle

Deselect Answer

14.45 cm

20.10 cm

13.33 cm

11.5 cm

None

27.

In a circle of radius 5 cm,AB and AC are two chords such that AB=AC=6c. The perpendicular distance of A from BC is

Topic: Chords and Perpendicular Distance

Deselect Answer

3.6 cm

4 cm

3 cm

6 cm

None

28.

AOB is a diameter of a circle with centre O and AC is a tangent to the circle at A. If ∠BOC = 130°, then find ∠ACO.

Deselect Answer

30°

40°

50°

80°

None

29.

In the given figure., from a point P, two tangents PT and PS are drawn to a circle with centre O such that ∠SPT = 120°, then:

Topic: Angle Between Tangents from an External Point

Deselect Answer

$\displaystyle OP=2PS$

$\displaystyle PS=2OP$

$\displaystyle OP=\dfrac{{PS}}{2}$

$\displaystyle OP=PS$

None

30.

From an external point P, tangents PA and PB are drawn to a circle with center O. If CD is the tangent to the circle at a point E and PA = 14 cm, find the perimeter of the △PCD.

Topic: Perimeter Involving Tangents

Deselect Answer

36 cm

28 cm

11 cm

44 cm

None

1 out of 30

Time's up

Class 10 Quiz Level 1 (Easy) – Circles

Welcome back