CBSE Class 9 Mathematics Circles VBQs

Question. The collection of all points in a plane which are at a fixed distance from a given point of the plane is called
(a) Centre
(b) Circumference
(c) Circle
(d) Radius
Answer : C

Question. AB, BC, CD and DA are four chords of a circle with centre O. If ∠AOB = 50°, ∠BOC = 150° and ∠COD = 85°, then the longest among the four chords is
(a) BC
(b) AB
(c) DA
(d) CD
Answer : A

Question. If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle is
(a) 15 cm
(b) 17 cm
(c) 16 cm
(d) 34 cm
Answer : B

Question. End points of chord lie
(a) Outside the circle
(b) Inside the circle
(c) On the circle
(d) None of these
Answer : C

Question. The points lying in which of the following don’t belong to the circular region of a circle
(a) Exterior of circle
(b) On the circle
(c) Interior of circle
(d) Both (a) and (c)
Answer : A

Question. The degree measure of circle is
(a) 180°
(b) 360°
(c) 90°
(d) 270°
Answer : B

Question. The two parts of the circle formed by a chord whose mid-point coincides with the centre are called
(a) Quadrants
(b) Semicircles
(c) Segments
(d) Sectors
Answer : B

Question. The length of the perpendicular from the centre of a circle of radius 13 cm on a chord of length 24 cm is
(a) 6 cm
(b) 5 cm
(c) 4 cm
(d) 3 cm
Answer : B

Question. AD is a diameter of a circle and AB is a chord.
If AD = 36 cm and AB = 26 cm, the distance of AB from the centre of the circle is
(a) 17.35 cm
(b) 15.45 cm
(c) 12.45 cm
(d) 8.35 cm
Answer : C

Question. AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is
(a) 17 cm
(b) 15 cm
(c) 4 cm
(d) 8 cm
Answer : D

Question. The angle in a semi circle measures
(a) 45°
(b) 60°
(c) 90°
(d) 36°
Answer : C

Question. Given a circle with centre O and smaller chord AB of length 5 cm and the longest chord CD of the circle of length 12 cm. The radius of the circle is
(a) 15 cm
(b) 6 cm
(c) 5 cm
(d) 3.5 cm
Answer : B

Question. Which of the following is the angle type in the major sector of a circle?
(a) acute angle
(b) obtuse angle
(c) reflex angle
(d) none of these
Answer : C

Question. The minute hand of a clock is at 12 and the hour hand is at 4. The angle between the hands of the clock is
(a) 120°
(b) 20°
(c) 30°
(d) 60°
Answer : A

Question. In the given figure, O is the centre of the circle. COD is an equilateral triangle. CD = AB, then ∠AOB =
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer : C

Question. Equal chords of a circle are equidistant from
(a) the centre
(b) an extremity of a diameter
(c) any point on the circumference
(d) any point on the diameter
Answer : A

Question. ABCD is a cyclic quadrilateral. If ∠A = (2x + 4)°, ∠B = (y + 10)°, ∠C = (4x – 4)° and ∠D = (5y + 20)°, then ∠A, ∠B, ∠C and ∠D respectively are
(a) 70°, 122°, 110°, 58°
(b) 60°, 105°, 120°, 75°
(c) 84°, 50°, 96°, 130°
(d) 64°, 35°, 116°, 145°
Answer : D

Question. The centre of the circle passing through the vertices of a right angled triangle lies
(a) inside the triangle
(b) outside the triangle
(c) on the hypotenuse
(d) none of these
Answer : C

Question. ABCD is a cyclic quadrilateral. If ∠A = 4x, ∠B = 3y, ∠C = 2x and ∠D = 15y, then x and y are equal to
(a) x = 25°, y = 20°
(b) x = 30°, y = 10°
(c) x = 20°, y = 18°
(d) x = 10°, y = 25°
Answer : B

Question. Number of circles that can be drawn passing through two points are
(a) one
(b) two
(c) infinite
(d) no circle can be drawn
Answer : C

Question. The line drawn through the centre of a circle to bisect a chord is ______ to the chord.
(a) Perpendicular
(b) Parallel
(c) Both (a) and (b)
(d) Can’t say
Answer : A

Case Based MCQs

Case I : Read the following passage and answer the questions from 1 to 5.
Three friends Amit, Mayank and Richa were playing with ball by standing on a circle at A, B and C point respectively. Richa throws a ball to Amit, Amit to Mayank and Mayank to Richa.
They all are equidistant from each other as shown in the figure.

Considering O as the centre of the circle, answer the following questions.

1. Which type of ΔABC is given in figure?
(a) Right angled triangle
(b) Equilateral triangle
(c) Isosceles triangle
(d) Scalene triangle
Answer : B

2. Measure of ∠ABC is
(a) 45°
(b) 60°
(c) 30°
(d) 90°
Answer : B

3. If AB = 6 cm, then BC + CA is equal to
(a) 12 cm
(b) 14 cm
(c) 15 cm
(d) 18 cm
Answer : A

4. Measure of ∠BOC is
(a) 90°
(b) 100°
(c) 120°
(d) 150°
Answer : C

5. Value of ∠OBC + ∠OCB is
(a) 30°
(b) 45°
(c) 90°
(d) 60°
Answer : A

Short Answer Type Questions

                                                                                      

                                                      

If the boundary wall is 200 m long

(a) How many circles can be drawn ?

(b) What values are inculcated in the students by this activity ?
Answer:  (a) 250  (b) Beauty

 

Question. A group of 66 students went for a picnic. They halted at a park for their lunch. They made a big circle and each child was 50 cm away from the other child along the circle.

 

 

                                                                                

(a) Find the radius of the circle they formed.

(b) What values do these students possess ?
Answer: (a) 5.25 m     (b) Co-operation, happiness

 

Question. An amusement fair was organised in a circular park for the children of slum clusters. Free food was supplied to them at 4 stalls situated at A, B, C and D as shown in the figure.

                                                                       

(a) Find the distance between any two adjacent food stalls if theradius of the park is 30 m.

(b) Are such activities helpful for society ? What are the other social issues for which such compaigns are required ?
Answer: (a) 30√ 2 m   (b) Yes, for the inmates of old age home, orphanages, handicapped children etc.

 

Question. Children of a colony decided to assist and help an old couple of the colony in developing their vacant plot as flower bed as shown here. The,radii of the two circles is 245 cm and 210 cm.

(a) Find the area of the grass cover.

(b) Which values are depicted by the children?
Answer: (a) 50050 sq. cm (b) Helpfulness

                                                                            

Question. 3 STD booths situated at A, B and C in the fig. are operated by handicapped persons. These three booths are equidistant from each other as shown in the figure.

                                                                                

(a) Find angle BOC

(b) Do you think employment provided to handicapped persons is important for the development of a society ? Justify your answer.
Answer: (a) 120°  (b) Yes

 

Question. During a practical activity in maths lab, students were using circular Geo board. The angle subtended by an arc at the centre is (2a+50°) Sakshi calculated angle BAC as (a+25°)

 

                                                                             

                                                                           

(a) Is her finding correct ? Justify it.

(b) Find angle BAC if a = 30

(c) Which values are depicted here ?
Answer: (a) Yes   (b) 55° (c) T r u t h ,scientific temper

 

Question. In a circle with centre O, ABCD is a cyclic quadrilateral.