Class 10 Practice – Level 3 – Set 2 – Circles

Total questions: 15

In the following figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT = 60°, What should be angle value of ∠PRQ.

Topic: Tangents and Chords in a Circle

120°

90°

140°

60°

None

In the given figure, two tangents PT and PS are drawn to a circle from an external point P with centre O and radius r. If OP = 2r, then find the value of ∠OTS and ∠OST?

Topic: Tangents to a Circle

30°, 30°

60°, 30°

90°, 60°

60°, 60°

None

A circle is touching the side BC of △ABC at P and touching AB and AC produced at Q and R respectively. What will be the value of AQ?

Topic: Incircle and its Tangents

AQ = $ \displaystyle \dfrac{1}{2}$ (perimeter of triangle ABC )

AQ = $ \displaystyle \dfrac{3}{2}$ (perimeter of triangle ABC )

AQ = $ \displaystyle \dfrac{1}{3}$ (perimeter of triangle ABC ).

AQ = $ \displaystyle \dfrac{1}{4}$ (perimeter of triangle ABC )

None

In the given figure, l and m are two parallel tangents to a circle with centre O, touching the circle at A and B respectively. Another tangent at C intersects the line l at D and m at E. Find ∠DOE.

Topic: Tangents and Lines

60°

90°

45°

30°

None

A triangle ABC is drawn to circumscribe a circle of radius 3 cm, such that are segments BD and DC are respectively of lengths 6 cm and 9 cm. If the area of △ABC is 54 $ \displaystyle \text{c}{{\text{m}}^{2}}$,What is the lengths of sides AB and AC?

Topic: Circumscribed Triangles

2 cm and 10 cm

4 cm and 16 cm

9 cm and 12 cm

5 cm and 15 cm

None

AB and CD are two perpendicular diameters of a circle with centre O, OD is the diameter of smaller circle. If OA = 7 cm, What should be the value of the area of the shaded region in the given figure?

Topic: Diameters of Circles

74.2 $ \displaystyle \text{c}{{\text{m}}^{2}}$

23.6 $ \displaystyle \text{c}{{\text{m}}^{2}}$

66.5 $ \displaystyle \text{c}{{\text{m}}^{2}}$

58.2 $ \displaystyle \text{c}{{\text{m}}^{2}}$

None

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: Tangents and radius

10 cm

12 cm

14 cm

16 cm

None

A tangent to a circle is perpendicular to the radius through the point of contact.

Topic: Tangents and radius

False

True

Cannot be predicted

Incomplete information

None

The length of tangent from an external point on a circle is:

Topic: Length of tangent

Always less than the radius of the circle

May or may not be greater than the radius of circle

Always greater than the radius of the circle.

None of the above

None

10.

In the given figure AC is a tangent to the circle with center O. If ∠ADB = 55°, What is the value of x and y?

Topic: Angle properties of tangents

x = 80° and y = 100°

x = 60° and y = 120°

x = 40° and y = 50°

x = 20° and y = 70°

None

11.

In the given figure, △ABC is circumscribing a circle, find the length of BC in cm?

Topic: Circumscribed circle and tangent segments

8 cm

15 cm

10 cm

6 cm

None

12.

A piece of wire 22 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its center. Find the radius of the circle. [ Use π = $ \displaystyle \dfrac{22}{7}$]

Topic: Arc Length and Circle Properties

18 cm

21 cm

28 cm

32 cm

None

13.

In the given figure, PQ is a chord of length 8 cm of a circle of radius 5 cm and centre O. The tangents at P and Q intersect at point T. Find the length of PT?

Topic: Tangents and Chords in a Circle

Number of Tangents from a Point on a Circle

$ \displaystyle \dfrac{{20}}{3}cm$

$ \displaystyle \dfrac{{10}}{4}cm$

$ \displaystyle \dfrac{{55}}{2}cm$

$ \displaystyle \dfrac{{10}}{9}cm$

None

14.

In the given figure, ABC is a right-angled triangle with AB = 6 cm and AC = 8 cm. A circle with centre O has been inscribed inside the triangle. Calculate the value of r, the radius of the inscribed circle.

Topic: Radius of an inscribed circle