CBSE Class 9 Mathematics Circles Worksheet Set 01

Question. Keeping his speed the same, John takes 1.5  times as much time to jog once along the outer edge of the circular track shown here as compared to the inner edge.
What is the width of the track if the radius of the inner edge is 24 m? 
 

A. 36 m
B. 24 m
C. 15 m
D. 12 m

Answer : D

Question. Triangle KLM is inscribed in the circle with centre O. If    m OLM = 50⁰and  m  KOM = 160⁰,what is the measure of LKO?

A. 20⁰
B. 30⁰
C. 40⁰
D. 50⁰

Answer : B

Question. O is the centre of the circle shown here
Note: The figure is not to scale.
What is   BCA?

A. 65⁰
B. 35⁰
C. 25⁰
D. 115⁰

Answer : C

Question. Swati cuts out three SEMI-CIRCULAR pieces of radius 5 cm from a large sheet of paper. She then sticks them on a piece of cardboard to form the design shown below in such a way that there is no overlap:
What is the perimeter of the shape (in cm)?

A. 15π
B. 30π
C. 15π+10
D. 30π+10

Answer : C

Question. The area of the shaded part of the quadrilateral is

A. 77 cm²
B. 98 cm²
C. 154 cm²
D. (Cannot say)

Answer : C

Question. The largest SEMICIRCLE that can be cut out of the rectangle shown here will have a radius of

A. 4 cm
B. 8 cm
C. 9 cm
D. 10 cm

Answer : B

Question. At what time between 9 o'clock and 10 o'clock does the minute hand of a clock overtake the hour hand?
A. at 9:30
B. between 9:46 and 9:48
C. between 9:48 and 9:50
D. between 9:50 and 9:52

Answer : C

Question. O is the centre of the circle shown below.What is the measure of ∠QPR ?

A. 30^∘
B. 105^∘
C. 210^∘
D. 150^∘

Answer : B

Question. Two circles have radii x cm and y cm respectively (x not equal to y) and the distance between their centres is d cm. If x - y = d, what will be the relative position of the two circles?

Answer : C

Question. What would be the time shown by this clock after the HOUR hand has turned by 8°?

A. 1:31
B. 1:38
C. 1:46
D. 2:52

Answer : C

Question. In the figure, QP is a diameter of the outermost circle and the centres of the other two circles also lie on QP. The radii of the three circles are in the ratio 4 : 2 : 1. 
What fraction of the outermost circle is shaded?

A. 1/2
B. 3/7
C. 4/11
D. 7/16

Answer : D

Question. Sania drew a quadrilateral PQRS in which the opposite angles were supplementary but the adjacent angles were not. What kind of quadrilateral was PQRS?
A. A trapezium
B. A rhombus
C. A parallelogram
D. A cyclic quadrilateral

Answer : D

Question. What will be the measure of angle y if 65% of the semi circular region is shaded?

A. 60°
B. 63°
C. 65°
D. 75°

Answer : B
 

Case Based MCQs

Case I : Read the following passage and answer the questions from 1 to 5.
Ankit visited in a mall with his father. He sees that three shops are situated at P, Q, R as shown in the figure from where they have to purchase things according to their need.
Distance between shop P and Q is 8 m, that of between shop Q and R is 10 m and between shop P and R is 6 m.

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

1. Find the radius of the circle.
(a) 5 m
(b) 7 m
(c) 14 m
(d) 8 m
Answer : A

2. Measure of ∠QPR is
(a) 60°
(b) 90°
(c) 120°
(d) 180°
Answer : B

3. Area of ΔPQR is
(a) 18 m²
(b) 20 m²
(c) 22 m²
(d) 24 m²
Answer : D

4. Length of the longest chord of the circle is
(a) 6 m
(b) 8 m
(c) 10 m
(d) 24 m
Answer : C

5. In figure, PSQP is known as
(a) Major segment
(b) Minor segment
(c) Major sector
(d) Minor sector
Answer : B

Case III : Read the following passage and answer the questions from 6 to 10.
Rohan is class 9th student. He did not attend school as his health is not fine since few days. At home, he open his Maths textbook and observe chapter circle. He was so much curious to know about the properties of circle. His father Mr Raman, who is also a good Mathematician helps Rohan to understand all properties one by one. At last, he ask some questions to Rohan for quick revision. Help Rohan to answer the following questions.

6. A circle can circumscribe a
(a) Rectangle
(b) Trapezium
(c) Triangle
(d) All of these
Answer : D

7. The perpendicular distance from the centre of the circle decreases when
(a) the length of the chord increases
(b) the length of the chord decreases
(c) Radius of circle is decreased
(d) Radius of circle is increased
Answer : A

8. The number of radii that can be drawn in a circle is
(a) 10
(b) 100
(c) 1000
(d) infinite
Answer : D

9. The distance from the centre of the circle to the longest chord is equal to
(a) (22/7) units
(b) 0 unit
(c) 1 unit
(d) 3 units
Answer : B

10. Angle formed by the equal arcs on the circumference of the circle
(a) are supplementary
(b) are equal
(c) are complimentary
(d) None of these
Answer : B

Assertion & Reasoning Based MCQs

Directions (Q. 1 to 5) : In these questions, a statement of Assertion is followed by a statement of Reason is given. Choose the correct
answer out of the following choices :
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

1. Assertion : In the given figure, O is the centre of the circle of radius 5 cm. If OP ⊥ AB, OQ ⊥ CD, AB || CD, AB = 6 cm and CD = 8 cm, then PQ = 6 cm.

Reason : Perpendicular bisectors of two chords of a circle intersect at its centre.
Answer : D

2. Assertion : AB and CD are two parallel chords of a circle whose diameter is AC. Then AB ≠ CD.
Reason : Perpendicular from the centre of a circle bisects the chord.
Answer : D

3. Assertion : The length of a chord which is at a distance of 5 cm from the centre of a circle of radius 10 cm is 17.32 cm.
Reason : The perpendicular from the centre of a circle to a chord bisects the chord.
Answer : A

4. Assertion : In a cyclic quadrilateral ABCD, ∠A – ∠C = 60°, then the smaller of two is 60°
Reason : Opposite angles of cyclic quadrilateral are supplementary.
Answer : A

5. Assertion : In an isosceles triangle ABC with AB = AC, a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BC.
Reason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilateral.
Answer : A

Please refer to attached file for CBSE Class 9 Mathematics Worksheet - Circles