Class 10 Practice – Level 1 – Circles

Total questions: 40

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

30 cm

34 cm

36 cm

40 cm

None

The tangent at any point of a circle is

Topic: Tangent to a Circle

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

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

Topic: Angle Between Chord and Tangent

52.5°

45°

62.5°

25°

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

60°

45°

120°

90°

None

In the given figure, O is the centre of circle, PQ is a chord and PT is tangent at P which makes an angle of 50° with PQ. ∠POQ is

Topic: Angle Between Chord and Tangent

130°

90°

100°

75°

None

The length PB = _________ cm.

Topic: Length of a Chord

None

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.

Topic: Angle Between Chord and Tangent

30°

40°

50°

80°

None

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

Topic: Length of a Chord

$ \displaystyle \text{CA}=2\sqrt{{{{\text{b}}^{2}}-{{\text{a}}^{2}}}}$

$ \displaystyle \text{BC}=2\sqrt{{{{\text{a}}^{2}}+{{\text{b}}^{2}}}}$

$ \displaystyle \text{AB}=2\sqrt{{{{\text{a}}^{2}}-{{\text{b}}^{2}}}}$

None of the above

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

90°

55°

67°

70°

None

10.

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

90°

61°

82°

72°

None

11.

What can be said about the tangents drawn at the end of a diameter of a circle?

Topic: Angle Between Diameter and Tangent

CD ∥ EF

DC ∥ FE

DF ∥ CE

AB ∥ EF

None

12.

Tangents PA and PB are drawn from an external point P to two concentric circle with centre O and radii 8 cm and 5 cm respectively, as shown in figure. If AP = 15 cm, then find the length of BP.

Topic: Tangents to Concentric Circles

14.33

18.94

16.25

10.36

None

13.

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

25 cm

30 cm

45 cm

50 cm

None

14.

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

25cm

56cm

33cm

72 cm

None

15.

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

True

False

More information is required

None of the above

None

16.

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

Topic: Angle Between Two Tangents

True

False

Cannot be determined

Sometimes true

None

17.

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

30 cm

28 cm

32 cm

25 cm

None

18.

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

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

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

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

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

None

19.

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 13 cm. Find the length of PQ.

Topic: Tangent Length with Given

11 cm

10 cm

12 cm

14 cm

None

20.

The length of the tangent to a circle from a point Q, which is 25 cm away from the center is 24 cm. What is the radius of the circle?

Topic: Radius from Tangent Length

10 cm

6 cm

4 cm

7 cm

None

21.

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

36 cm

28 cm

11 cm

44 cm

None

22.

Find the area of a quadrant of a circle whose circumference is 88cm.

Topic: Area of a Sector of a Circle

175 sq. cm .

154 sq. cm .

166 sq. cm .

146 sq. cm

None

23.

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

55°

90°

30°

70°

None

24.

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

Topic: Properties of Chords in a Circle

BE = EC

DF = BC

DB = FC

EC = DF

None

25.

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

$ \displaystyle 2\sqrt{4}$ cm

$ \displaystyle 6\sqrt{4}$ cm

$ \displaystyle 4\sqrt{2}$ cm

$ \displaystyle 5\sqrt{2}$ cm

None

26.

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

Topic: Length of Tangents from an External Point

True

False

More information is required

Cannot be predicted

None

27.

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

$\displaystyle OP=2PS$

$\displaystyle PS=2OP$

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

$\displaystyle OP=PS$

None

28.

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

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

$\displaystyle 10\text{ cm}$

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

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

None

29.

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

Topic: Length of Tangents from an External Point

Yes

More information required

Cannot be predicted

None

30.

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

14.45 cm

20.10 cm

13.33 cm

11.5 cm

None

31.

How many tangents can a circle have?

Topic: Number of Tangents to a Circle

Fifty tangents

Hundred tangents

Infinite tangents

No tangents

None

32.

In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠ PTQ is equal to:

Topic: Angle Between Two Tangents

180°

30°

90°

70°

None

33.

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠POA is equal to.

Topic: Tangent and Radius

70°

60°

40°

50°

None

34.

A tangent intersects the circle at:

Topic: Point of Contact of a Tangent

Many points

Two distinct points

One point

None of the above

None

35.

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

True

False

Cannot be predicted

More information required

None

36.

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

3.6 cm

4 cm

3 cm

6 cm

None

37.

PA and PB are tangents to the circle with centre O from an external point P, touching the circle at A and B respectively. Then the quadrilateral AOBP is

Topic: Tangents and Quadrilateral Properties

Non-cyclic

Cyclic

Kite

Rhombus

None

38.

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

3 cm

6 cm

9 cm

1 cm

None

39.

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

Topic: Parallel Tangents of a Circle

Only one

Two

Four

Infinite

None

40.

The parallelogram circumscribing a circle will be a:

Topic: Circumscribing Parallelogram Properties

Rhombus

Rectangle

Square

Trapezium

None

1 out of 40

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Class 10 Practice – Level 1 – Circles

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