CBSE Class 10 Mathematics Circles Worksheet Set D

Read and download the CBSE Class 10 Mathematics Circles Worksheet Set D in PDF format. We have provided exhaustive and printable Class 10 Mathematics worksheets for Chapter 10 Circles, designed by expert teachers. These resources align with the 2025-26 syllabus and examination patterns issued by NCERT, CBSE, and KVS, helping students master all important chapter topics.

Chapter-wise Worksheet for Class 10 Mathematics Chapter 10 Circles

Students of Class 10 should use this Mathematics practice paper to check their understanding of Chapter 10 Circles as it includes essential problems and detailed solutions. Regular self-testing with these will help you achieve higher marks in your school tests and final examinations.

Class 10 Mathematics Chapter 10 Circles Worksheet with Answers

 

Circles

Q.- If O is the centre of a circle, PQ is a chord and tangent PR at P makes an angle of with PQ, then POQ is equal to 
WT_circles test 9
a. 110°
b. 120°
c. 100°
d. 90°
 
Ans- b. 120°
Explanation: Here RPO = 90°
∠RPQ = 60° (given)
∴ ∠OPQ = 90° - 60° = 30° PQO = 30° Also [Opposite angles of equal radii] Now,
In triangle OPQ,
∠OPQ +∠ PQO + ∠QOP =180°
=> 30° + 30° + QOP = 180°
=> ∠QOP = 120°
 
Q.- In the given figure, if OQ = 3 cm, OP = 5 m, then the length of PR is 
WT_circles test 10
a. 4 cm
b. 3 cm
c. 5 cm
d. 6 cm
 
Ans- a. 4 cm
Explanation: Here Q = 90° [Angle between tangent and radius through the point of contact]
Now, in right angled triangle OPQ,
OP2 = OQ2 + PQ2
(5)2 = (3)2 + PQ2
PQ2 = 25 - 9 = 16
PQ = 4 cm
But PQ = PR [Tangents from one point to a circle are equal]
Therefore, PR = 4 cm
 
Q.-  In figure, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA ⊥ PB, then the length of each tangent is: 
WT_circles test 11
a. 5 cm
b. 3 cm
c. 4 cm
d. 8 cm
 
Ans- c. 4 cm
WT_circles test 12
Explanation:
Construction: Joined AC and BC. Here CA⊥AP and CB ⊥ BP and PA ⊥ PB Also
AP = PB
Therefore, BPAC is a square. AP = PB = BC = 4 cm
 
Q.- The length of tangent PQ, from an external point Q is 24 cm. If the distance of the point Q from the centre is 25 cm, then the diameter of the circle is 
WT_circles test 14
a. 15 cm
b. 14 cm
c. 12 cm
d. 7 cm
 
Ans- 5. b. 14 cm
WT_circles test 13
Explanation:
Here ∠ OPQ = 90o [Angle between tangent and radius through the point of contact]
OQ2 = OP2 + PQ2 (25)2 = OP2 + (24)2
OP2 = 625 - 576 OP2 = 49
OP2 = 49 OP = 7 cm
Therefore, the diameter = 2 OP = 2 7 = 14 cm
 
Q.- What term will you use for a line which intersect a circle at two distinct points? 

Ans-  A line that interests a circle at two points in a circle is called a Secant.

Q.-In the fig. there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm find the length of PS. (1)
Ans- PQ = PR = 5 cm ( Length of Tangents from same external point are always equal) and PQ = QS (perpendicular from center of the circle to the chord bisects the chord)
 PS = 2PQ
= 2×5 =10cm
 
Q.-  Find the distance between two parallel tangents of a circle of radius 3 cm.
WT_circles test 15
Ans-  Distance between two parallel tangents = diameter = PQ
PQ = OP + OQ = 3 + 3 = 6cm
The total distance between two parallel tangents lines is 6 cm.

 

Please click the below link to access CBSE Class 10 Mathematics Circles Worksheet Set D

CBSE Mathematics Class 10 Chapter 10 Circles Worksheet

Students can use the practice questions and answers provided above for Chapter 10 Circles to prepare for their upcoming school tests. This resource is designed by expert teachers as per the latest 2026 syllabus released by CBSE for Class 10. We suggest that Class 10 students solve these questions daily for a strong foundation in Mathematics.

Chapter 10 Circles Solutions & NCERT Alignment

Our expert teachers have referred to the latest NCERT book for Class 10 Mathematics to create these exercises. After solving the questions you should compare your answers with our detailed solutions as they have been designed by expert teachers. You will understand the correct way to write answers for the CBSE exams. You can also see above MCQ questions for Mathematics to cover every important topic in the chapter.

Class 10 Exam Preparation Strategy

Regular practice of this Class 10 Mathematics study material helps you to be familiar with the most regularly asked exam topics. If you find any topic in Chapter 10 Circles difficult then you can refer to our NCERT solutions for Class 10 Mathematics. All revision sheets and printable assignments on studiestoday.com are free and updated to help students get better scores in their school examinations.

Where can I download latest CBSE Printable worksheets for Class 10 Mathematics Chapter 10 Circles

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Are there any websites that offer free test sheets for Class 10 Mathematics Chapter 10 Circles

Yes, studiestoday.com provides all latest NCERT Chapter 10 Circles Class 10 Mathematics test sheets with answers based on the latest books for the current academic session

What topics are covered in CBSE Class 10 Mathematics Chapter 10 Circles worksheets?

CBSE Class 10 Mathematics Chapter 10 Circles worksheets cover all topics as per the latest syllabus for current academic year.

How can I use worksheets to improve my Class 10 Mathematics scores?

Regular practice with Class 10 Mathematics worksheets can help you understand all concepts better, you can identify weak areas, and improve your speed and accuracy.