CBSE Class 10 Mathematics Circles VBQs

Question. If radii of two concentric circles are 4 cm and 5 cm, then length of each chord of one circle, which is tangent to the other circle, is 
(a) 3 cm
(b) 6 cm
(c) 9 cm
(d) 1 cm
Answer : B

Question. The length of tangent from an external point P on a circle with centreO is always less than OP.
(a) True
(b) False
(c) Can’t determined
(d) None of these
Answer : A

Question. The length of the tangents to the circle from a point at any distance of 5 cm from centre of the circle of radius 3 cm is
(a) 2 cm
(b) 4 cm
(c) 8 cm
(d) None of these
Answer : B

Question. The length of the tangent drawn from a point 8 cm away from the centre of circle of radius 6 cm is
(a) 7 cm
(b) 2 7 cm
(c) 10 cm
(d) 5 cm
Answer : B

Question. PQ is a tangent to a circle with centre O at the point P. If ΔOPQ is an isosceles triangle, then ∠OPQ is equal to
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer : B

Case Based MCQs

A. A playground is in the shape of a triangle with right angle at B, AB = 3m and BC = 4m. A pit was dig inside it such that it touches the walls AC,BC and AB at P,Q and R, respectively such that AP = x m.

Based on the above information, answer the following questions.

Question. The value of AR =
(a) 2xm
(b) x / 2 m
(c) xm
(d) 3x m
Answer : C

Question. The value of BQ=
(a) 2x m
(b) (3 − x)m
(c) (2 − x)m
(d) 4x m
Answer : B

(iii) The value of CQ=
(a) (4 + x)m
(b) (5 − x)m
(c) (1 + x)m
(d) Both (b) and (c)
Answer : D

Question. Which of the following is correct?
(a) Quadrilateral AROP is a square
(b) Quadrilatera lBROQis a square
(c) Quadrilateral CQOP is a square
(d) None of the above
Answer : B

Question. Radius of the pit is
(a) 1 m
(b) 3 m
(c) 4 m
(d) 5 m
Answer : A

B. A student draws two circles that touch each other externally at point K with centres A and B and radii 6 cmand 4 cm, respectively as shown in the figure.

Based on the above information, answer the following questions.

Question. The value of PA =
(a) 10 cm
(b) 5 cm
(c) 13 cm
(d) Can’t be determined
Answer : C

Question. The value of BQ=
(a) 4 cm
(b) 5 cm
(c) 6 cm
(d) 18 cm
Answer : B

Question. The value of PK =
(a) 13 cm
(b) 15 cm
(c) 16 cm
(d) 18 cm
Answer : C

Question. The value of QY =
(a) 2 cm
(b) 5 cm
(c) 1 cm
(d) 3 cm
Answer : C

Question. If two circles touch externally, then the number of common tangents can be drawn is
(a) 1
(b) 2
(c) 3
(d) None of these
Answer : B

Question. A group of students of the Heritage Club of a college took up the work of restoring an old circular shaped monument in their neighbourhood. To help them in their work a rope of 10m length was tied from the edge of the circular dome to a pole tangentially which is 26 m from the centre of the dome.

Contextual Question:

What is the radius of the circular dome?

Value based Question:

What values are imbibed by the students in this initiative?

Key Points.

* Protection of monuments.

* Appreciations for the culture.

* Respect for heritage

Question. Raj tied a stone to the end of a string 80cm long and swirled it in a circular motion by holding the other end. At one instance it slipped out of his hand and the stone flew tangentially and hit the glass window pane of the neighbourhood house at a distance of 1.7m from him.

Contextual Question:

Through what distance did the stone move before hitting the window?

Value Based Question

As a responsible student would you encourage playing such games? Justify.

Key Points.

* No. it is dangerous as it might hurt someone.

 * No it might bring some damage.

Question. For the inauguration of the Eco-Club of a school , Badges were given to volunteers . Sudha made these badges in the shape of a triangle with a circle inscribed in it (As given in the figure). A message supporting tree plantation was written in the circle. The length of side BC is 14 cm.

Contextual Question: 

Calculate the length of sides AB and AC.

Value Based Question 

What values are imbibed by having such clubs in schools?

Key Points.

• Team Work

•  Social responsibility

•  Awareness of tree plantation

• Commitment.

Question. For a Science Exhibition Rahul presented a Diagrammatic representation of Rain water harvesting as a Project. AB and AC are the pipes of 5m long is bringing water from the terrace of a building . (as in the Figure) The triangular space is developed as a garden.

Contextual Question: 

What is the perimeter of the triangular garden.

Value Based Question 

What qualities do you think is encouraged by such exhibitions?

Key Points.

• Creativity

• Encouraging greenery

• Saving water

• Team work

Question. Mr.Sharma constructed a circular tank to serve as a bird bath. He also made a fencing in the shape of a quadrilateral, the sides touching the circular tank.

Contextual Question 

If 3 sides are 6m, 7m and 4m find the length of the 4th side.

Value Based Question :

              What values does Mr. Sharma depict through his action.

Key Points:

• Compassion

• Care towards nature

• Love for Creatures

Question. As a part of a campaign a huge balloon with message of awareness of cancer was displayed from the terrace of a tall building. It was held by strings of length 9m each and inclined at an angle of 600 at the point where it was tied as shown in the figure.

Contextual Question :

What is the length AB.

Value Based Question :

What do you think of such campaign? Should youngsters be involved more in such campaigns.

Key Points:

• Creating awareness.

• Taking initiative

Please refer to attached file for CBSE Class 10 Mathematics VBQs - Circles