CBSE Class 10 Mathematics Circles Worksheet Set F

Access the latest CBSE Class 10 Mathematics Circles Worksheet Set F. We have provided free printable Class 10 Mathematics worksheets in PDF format, specifically designed for Chapter 10 Circles. These practice sets are prepared by expert teachers following the 2025-26 syllabus and exam patterns issued by CBSE, NCERT, and KVS.

Chapter 10 Circles Mathematics Practice Worksheet for Class 10

Students should use these Class 10 Mathematics chapter-wise worksheets for daily practice to improve their conceptual understanding. This detailed test papers include important questions and solutions for Chapter 10 Circles, to help you prepare for school tests and final examination. Regular practice of these Class 10 Mathematics questions will help improve your problem-solving speed and exam accuracy for the 2026 session.

Download Class 10 Mathematics Chapter 10 Circles Worksheet PDF

 

CIRCLES
 
Q.- In Fig., if AB = AC, prove that BE = EC
Circles notes 11
 
Sol. Since tangents from an exterior point to a circle are equal in length 
∴ AD = AF     [Tangents from A]
BD = BE       [Tangents from B]
CE = CF       [Tangents from C]
Now,
AB = AC
=> AB – AD = AC – AD
[Subtracting AD from both sides]
=> AB – AD = AC – AF [Using (i)]
=> BD = CF    => BE = CF [Using (ii)]
=> BE = CE [Using (iii)]
 
Q.- In fig. XP and XQ are tangents from X to the circle with centre O. R is a point on the circle.
Circles notes 12
Prove that, XA + AR = XB + BR.
 
Sol. Since lengths of tangents from an exterior
point to a circle are equal.
∴ XP = XQ      .... (i) [From X]
AP = AR         .... (ii) [From A]
BQ = BR         .... (iii) [From B]
Now, XP = XQ
=> XA + AP = XB + BQ
=> XA + AR = XB + BR
[Using equations (i) and (ii)]
 
SECTION A:
 
1. A line touches a circle of radius 4 cm. Another line is drawn which is tangent to the circle. If the two lines are parallel then find the distance between them.
 
2. From a point P, which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR are drawn to the circle. Find the area of the quadrilateral PQOR.
 
3. In fig 1, if O is centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then find∠POQ.
 
4. In the figure 2, QR is a common tangent to given circle which meet at T. Tangent at T meets QR at P. If QP = 3.8 cm, then find the length of QR.
 
5. In fig. 3, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm, BC = 7 cm, then find the length of BR.
CBSE Class 10 Mathematics Circles Worksheet Set F1
 
6. Point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then find the radius of the circle.
 
7. TP and TQ are two tangents to a circle with centre O such that ∠POQ = 110⁰. Then find ∠PTQ.
 
8. In the figure , QR is a common tangent to given circle which meet at T. Tangent at T meets QR at P. If QP = 3.8 cm, then find the length of QR.
CBSE Class 10 Mathematics Circles Worksheet Set F2
 
9. If the angle between two radii of a circle is 100⁰, find the angle between the tangents at the ends of the radii.
 
10. From a point P which is at a distance of 13 cm from the center of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then find the area of the quadrilateral PQOR.
 
SECTION B :
 
1. Two concentric circles of radii a and b , where a>b are given. Find the length of chord of the larger circle which touches the smaller circle.
 
2. If d1, d2(d2>d1) be diameters of two concentric circles, c be the length of a chord of the circle which is tangent to the other circle, prove that d2 2 = c2 + d12.
 
3. If two tangents inclined at an angle 60⁰ are drawn to a circle of radius 3 cm, find the length of each tangent.
 
4. PA and PB are two tangents drawn from an external point P to a circle with centre O. If OP is equal to diameter of the circle, prove that ΔABP is equilateral.
 
5. A circle touches the side AC of ΔABC at P, touches BC at Q and AB at R. Show thatAC + AR = BC + BR.
CBSE Class 10 Mathematics Circles Worksheet Set F3
 
6. If two tangents inclined at an angle 60⁰ are drawn to a circle of radius 3 cm, find the length of each tangent.
 
7. Two parallel lines touch a circle at points A and B separately. If area of the circle is 25 cm2, then find the length of AB.
 
8. In figure, if CP = 11 cm and BC = 7 cm, then find the length of BR.
CBSE Class 10 Mathematics Circles Worksheet Set F4
 
9. In the given figure , BOA is a diameter of a circle and the tangent at a point P meets BA produced at T. If ∠PBO = 30°, what is the measure of ∠PTA?
CBSE Class 10 Mathematics Circles Worksheet Set F5
 
10. In fig , a tangent PT is drawn parallel to a chord AB of a circle, as shown in given figure. Prove that APB is an isosceles triangle.
CBSE Class 10 Mathematics Circles Worksheet Set F6
 
SECTION C: 
 
1. In figure, a triangle ABC is drawn to circumscribe a circle of radius 10 cm such that the segments BP and PC into which BC is divided by the point of contact P, are of lengths 15 cm and 20 cm respectively. If the area of ΔABC is 525 cm2, then find the lengths of sides AB and AC.
CBSE Class 10 Mathematics Circles Worksheet Set F7
 
2. If angle between two tangents PT and QT drawn from a point T to a circle of radius r and centre O is 60⁰, then prove that PT = 3r.

 

Please click on below link to download CBSE Class 10 Mathematics Circles Worksheet Set F

Chapter 01 Real Numbers
CBSE Class 10 Mathematics Real Numbers And Polynomials Worksheet
CBSE Class 10 Mathematics Real Numbers Worksheet Set A
CBSE Class 10 Mathematics Real Numbers Worksheet Set B
CBSE Class 10 Mathematics Real Numbers Worksheet Set C
CBSE Class 10 Mathematics Real Numbers Worksheet Set D
CBSE Class 10 Mental Maths Real Numbers Worksheet
CBSE Class 10 Mental Maths Real Numbers Worksheet in Hindi
Chapter 02 Polynomials
CBSE Class 10 Mathematics Polynomials Worksheet Set A
CBSE Class 10 Mathematics Polynomials Worksheet Set B
CBSE Class 10 Mathematics Polynomials Worksheet Set C
CBSE Class 10 Mathematics Polynomials Worksheet Set D
CBSE Class 10 Mathematics Polynomials Worksheet Set E
CBSE Class 10 Mathematics Probability And Constructions Worksheet Set A
CBSE Class 10 Mathematics Probability And Constructions Worksheet Set B
CBSE Class 10 Mathematics Probability Worksheet Set A
CBSE Class 10 Mental Maths Polynomials Worksheet
CBSE Class 10 Mental Maths Polynomials Worksheet in Hindi
Chapter 03 Pair of Linear Equations in Two Variables
CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set A
CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set B
CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set C
CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set D
CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set E
CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set F
CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set G
CBSE Class 10 Mental Maths Pair of Linear Equations in Two Variables Worksheet
CBSE Class 10 Mental Maths Pair of Linear Equations in Two Variables Worksheet in Hindi
Chapter 04 Quadratic Equation
CBSE Class 10 Mathematics Quadratic Equations Worksheet Set A
CBSE Class 10 Mathematics Quadratic Equations Worksheet Set B
CBSE Class 10 Mathematics Quadratic Equations Worksheet Set C
CBSE Class 10 Mathematics Quadratic Equations Worksheet Set D
CBSE Class 10 Mathematics Quadratic Equations Worksheet Set E
CBSE Class 10 Mental Maths Quadratic Equations Worksheet
CBSE Class 10 Mental Maths Quadratic Equations Worksheet in Hindi
Chapter 05 Arithmetic Progression
CBSE Class 10 Arithmetic Progression Printable Worksheet Set A
CBSE Class 10 Arithmetic Progression Printable Worksheet Set B
CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set A
CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set B
CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set C
CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set D
CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set E
CBSE Class 10 Mental Maths Arithmetic Progressions Worksheet
CBSE Class 10 Mental Maths Arithmetic Progressions Worksheet in Hindi
Chapter 06 Triangles
CBSE Class 10 Mathematics Triangles Worksheet Set A
CBSE Class 10 Mathematics Triangles Worksheet Set B
CBSE Class 10 Mathematics Triangles Worksheet Set C
CBSE Class 10 Mathematics Triangles Worksheet Set D
CBSE Class 10 Mathematics Triangles Worksheet Set E
CBSE Class 10 Mental Maths Similar Triangles Worksheet
CBSE Class 10 Mental Maths Similar Triangles Worksheet in Hindi
Chapter 07 Coordinate Geometry
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set A
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set B
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set C
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set D
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set E
CBSE Class 10 Mental Maths Coordinate Geometry Worksheet
CBSE Class 10 Mental Maths Coordinate Geometry Worksheet in Hindi
Chapter 08 Introduction to Trigonometry
CBSE Class 10 Introduction to Trigonometry Worksheet Set A
CBSE Class 10 Mathematics Introduction to Trigonometry Worksheet Set B
CBSE Class 10 Mathematics Introduction to Trigonometry Worksheet Set C
CBSE Class 10 Mathematics Introduction to Trigonometry Worksheet Set D
CBSE Class 10 Mathematics Introduction to Trigonometry Worksheet Set E
CBSE Class 10 Mathematics Introduction to Trigonometry Worksheet Set F
Chapter 09 Some Applications of Trigonometry
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set A
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set B
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set C
CBSE Class 10 Mental Maths Some Applications of Trigonometry Worksheet
CBSE Class 10 Mental Maths Some Applications of Trigonometry Worksheet in Hindi
CBSE Class 10 Some Applications of Trigonometry Worksheet Set B
Chapter 10 Circles
CBSE Class 10 Mathematics Circles Worksheet Set A
CBSE Class 10 Mathematics Circles Worksheet Set B
CBSE Class 10 Mathematics Circles Worksheet Set C
CBSE Class 10 Mathematics Circles Worksheet Set D
CBSE Class 10 Mathematics Circles Worksheet Set E
CBSE Class 10 Mathematics Circles Worksheet Set F
CBSE Class 10 Mathematics Circles Worksheet Set G
CBSE Class 10 Mental Maths Areas Related To Circle Worksheet
CBSE Class 10 Mental Maths Circle Worksheet
CBSE Class 10 Mental Maths Circle Worksheet in Hindi
Chapter 11 Areas related to Circles
CBSE Class 10 Mathematics Area Related To Circle Worksheet Set A
CBSE Class 10 Mathematics Area Related To Circle Worksheet Set B
CBSE Class 10 Mathematics Area Related To Circle Worksheet Set C
CBSE Class 10 Mathematics Area Related To Circle Worksheet Set D
CBSE Class 10 Mental Maths Areas Related To Circle Worksheet in Hindi
Chapter 12 Surface Area and Volume
CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set A
CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set B
CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set C
CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set D
CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set E
CBSE Class 10 Mental Maths Surface Areas And Volumes Worksheet
CBSE Class 10 Mental Maths Surface Areas And Volumes Worksheet in Hindi
Chapter 13 Statistics
CBSE Class 10 Mathematics Statistics Worksheet Set A
CBSE Class 10 Mathematics Statistics Worksheet Set B
CBSE Class 10 Mathematics Statistics Worksheet Set C
CBSE Class 10 Maths Statistics And Probabilty Worksheet
CBSE Class 10 Mental Maths Statistics And Probabilty Worksheet
CBSE Class 10 Mental Maths Statistics And Probabilty Worksheet in Hindi
Chapter 14 Probability
CBSE Class 10 Mathematics Probability And Constructions Worksheet Set A
CBSE Class 10 Maths Probabilty Worksheet
z More Worksheets for Class 10 Mathematics
CBSE Class 10 Mathematics Question Bank
CBSE Class 10 Mathematics Worksheet Set A Solved
CBSE Class 10 Mathematics Worksheet Set B Solved
CBSE Class 10 Mathematics Worksheet Set C Solved
CBSE Class 10 Mathematics Worksheet Set D
CBSE Class 10 Mathematics Worksheet Set E
CBSE Class 10 Mathematics Worksheet Set F
~ Class 10 Mathematics (Old Chapters)
CBSE Class 10 Mental Maths Geometrical Constructions Worksheet
CBSE Class 10 Mental Maths Geometrical Constructions Worksheet in Hindi
CBSE Class 10 Mental Maths Geometrical Constructions Worksheet Set A

Important Practice Resources for Class 10 Mathematics

Chapter 10 Circles CBSE Class 10 Mathematics Worksheet

Students can use the Chapter 10 Circles practice sheet provided above to prepare for their upcoming school tests. This solved questions and answers follow the latest CBSE syllabus for Class 10 Mathematics. You can easily download the PDF format and solve these questions every day to improve your marks. Our expert teachers have made these from the most important topics that are always asked in your exams to help you get more marks in exams.

NCERT Based Questions and Solutions for Chapter 10 Circles

Our expert team has used the official NCERT book for Class 10 Mathematics to create this practice material for students. After solving the questions our teachers have also suggested to study the NCERT solutions  which will help you to understand the best way to solve problems in Mathematics. You can get all this study material for free on studiestoday.com.

Extra Practice for Mathematics

To get the best results in Class 10, students should try the Mathematics MCQ Test for this chapter. We have also provided printable assignments for Class 10 Mathematics on our website. Regular practice will help you feel more confident and get higher marks in CBSE examinations.

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

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