The NCERT Exemplar Class 10 Maths Circles book is a free, download-ready problem set, mapped to the 2026-27 NCERT syllabus. This page bundles the official Exemplar PDF with a question-type map, a difficulty guide and a study plan for harder CBSE-style practice on tangents, chords and circle theorems.
- CBSE Weightage: Circles is part of the Geometry unit, worth 15 marks in the Class 10 board paper (shared with Triangles).
- Exemplar Problems: 36 unsolved questions across 4 exercises (Exercise 10.1 to Exercise 10.4) plus a solved sample section.
- Question types: MCQ, reasoning (true or false with justification), short answer and long answer.
Also Check:
Watch Circles Class 10 Maths Explained
Source: Magnet Brains on YouTube
How This Exemplar PDF Helps You
This download wraps the official PDF with the maps you need for the board exam.
- Concept Recap Card: a one-screen summary of tangent-radius perpendicularity, equal tangents, and the two key circle theorems.
- Question-Type Tagging: every problem is tagged MCQ, reasoning, short answer or long answer, so you can drill one type at a time.
- Difficulty Flagging: each exercise is rated against the matching textbook exercise.
- Board-Style Map: each long-answer problem is matched to the CBSE style it resembles.
What Is Inside the Book
The Circles Exemplar is one connected problem set. It opens with a concepts page, then moves through five lettered sections. The table maps each section to its question range.
| Section | Questions | Type | What It Covers |
|---|---|---|---|
| (A) Main Concepts and Results | - | Theory recap | Tangent-radius perpendicularity, equal tangents, and the two main circle theorems |
| (B) Exercise 10.1 | Q1 to Q10 | MCQ | Tangent properties, number of tangents from a point, and quick angle work using the tangent-radius right angle |
| (C) Exercise 10.2 | Q1 to Q10 | True or False, with reason | Tangent and secant properties, equal tangent lengths, and when a line is a tangent or a chord |
| (D) Exercise 10.3 | Q1 to Q9 | Short Answer | Tangent lengths, angles in tangent-chord figures, and short proofs using equal tangents |
| (E) Exercise 10.4 | Q1 to Q7 | Long Answer | Multi-step proofs using both theorems, two-circle common tangents, and HOTS angle chasing |
Question-Type Distribution in Circles Class 10 Maths
The table splits the 36 problems across four types. Exercise 10.3 and 10.4 carry the most board value.
| Type | Exercise | Count | Best For |
|---|---|---|---|
| MCQ | Exercise 10.1 | 10 | 1-mark board MCQs and quick recall of tangent properties and angles |
| Reasoning (True or False) | Exercise 10.2 | 10 | Assertion-reason items on tangent-secant links, equal tangents, and tangent-chord angles |
| Short Answer | Exercise 10.3 | 9 | 2 and 3-mark problems on tangent lengths, angles, and short proofs |
| Long Answer | Exercise 10.4 | 7 | 5-mark multi-step proofs using both theorems and two-circle common tangents |
Why the Exemplar Matters for Circles
The Exemplar uses the same ideas as the textbook but raises the bar. It adds a second circle, combines both theorems in one proof, and brings angle-chasing where each step must be justified.
- Two-Tangent Proofs: Boards regularly set one problem on equal tangents from an external point. Exercise 10.4 Q1 to Q4 train it.
- Combined-Theorem Problems: A chord meeting a tangent, or a secant-tangent pair from one point, is a repeat board topic. Exercise 10.3 Q5 to Q9 drill it.
- Two-Circle Problems: Exercise 10.4 Q5 to Q7 train common-tangent problems with two circles of different radii.
Exemplar vs Textbook Difficulty
The same idea gets a softer test in the textbook and a harder one in the Exemplar. The table shows three cases.
| Concept | NCERT Textbook Style | NCERT Exemplar Style |
|---|---|---|
| Tangent Length from External Point | "A point P is 13 cm from the centre of a circle of radius 5 cm. Find the length of the tangent from P to the circle." | "Two tangents PA and PB are drawn to a circle with centre O. If angle APB = 80 degrees, find angle OAB. Justify each step using named circle theorems." |
| Tangent-Radius Angle | "A tangent PQ is drawn from an external point P to a circle with centre O such that OQ = 4 cm and angle OPQ = 30 degrees. Find PQ." | "From a point P outside a circle, two tangents PA and PB are drawn to the circle. Prove that angle PAB = angle PBA. Hence deduce the value of angle OAB in terms of angle APB." |
| Number of Tangents | "Prove that the tangents drawn at the ends of a diameter of a circle are parallel." | "AB is a chord of a circle and P is a point on the major arc. A tangent is drawn at A. Prove that angle between tangent AT and chord AB equals the angle in the alternate segment (angle APB)." |
The Exemplar always adds a layer: a proof, an angle-chasing step, or an algebraic unknown. Practise only the textbook and you can lose 3 to 5 marks per board proof, because the paper now wants the theorem named at each step.
Full worked solutions: Circles Class 10 Maths NCERT Exemplar Solutions
How to Use the Exemplar with the Textbook
The Exemplar does not replace the textbook. Interleave them, and a three-day plan keeps the load even.
- Day 1, theorems and MCQ: read the textbook on tangent-radius perpendicularity and equal tangents. Then do Exercise 10.1 Q1 to Q6 and Exercise 10.2 Q1 to Q5.
- Day 2, short-answer proofs: finish Exercise 10.1 Q7 to Q10 and Exercise 10.2 Q6 to Q10, then do Exercise 10.3 Q1 to Q9 on a 35-minute timer.
- Day 3, long answers and two circles: do Exercise 10.4 Q1 to Q7 on a 50-minute timer. Name the theorem and reason at each step.
Related Links:
PDF Formats and Languages
The Circles Exemplar PDF comes in formats for different revision styles. The table shows what each one is best for.
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading and quick revision between classes | 1-2 MB |
| HD PDF | Print-ready desk study and clean photocopies | 3-5 MB |
| Hindi-medium edition | Hindi-medium students; same problem numbering | 1-2 MB |
The Circles Exemplar PDF and its Hindi-medium edition use the same notation and numbering as the printed 2026-27 release. A few points to know:
- NCERT-faithful: every problem matches the printed Exemplar line for line, including the solved samples.
- Solutions separate: step-by-step answers live on the linked Exemplar Solutions page.
- State-board alignment: state boards share the same content; only the exercise numbers may differ.
More Circles Resources
NCERT Exemplar Book PDF for Class 10 Maths: All Chapters
Download any other chapter's Exemplar Book PDF for the 2026-27 cycle using the table below.
| Chapter | Exemplar Book PDF |
|---|---|
| Chapter 1 | Real Numbers NCERT Exemplar Book PDF |
| Chapter 2 | Polynomials NCERT Exemplar Book PDF |
| Chapter 3 | Pair of Linear Equations in Two Variables NCERT Exemplar Book PDF |
| Chapter 4 | Quadratic Equations NCERT Exemplar Book PDF |
| Chapter 5 | Arithmetic Progressions NCERT Exemplar Book PDF |
| Chapter 6 | Triangles NCERT Exemplar Book PDF |
| Chapter 7 | Coordinate Geometry NCERT Exemplar Book PDF |
| Chapter 8 | Introduction to Trigonometry NCERT Exemplar Book PDF |
| Chapter 9 | Some Applications of Trigonometry NCERT Exemplar Book PDF |
| Chapter 11 | Areas Related to Circles NCERT Exemplar Book PDF |
| Chapter 12 | Surface Areas and Volumes NCERT Exemplar Book PDF |
| Chapter 13 | Statistics NCERT Exemplar Book PDF |
| Chapter 14 | Probability NCERT Exemplar Book PDF |
Student Feedback
In a March 2026 survey of 9,140 Class 10 students, 79% said the long-answer tangent proofs in Exercise 10.4 were the hardest part, since they need the right auxiliary line and both theorems together. The average student lost 2.6 marks by confusing the tangent-radius theorem with the chord-bisector theorem. Toppers said finishing all 36 problems made combined tangent-chord questions feel routine in the board exam.
Source: Collegedunia March 2026 survey of 9,140 Class 10 Circles students.
| Resource | Link |
|---|---|
| NCERT Solutions | Circles NCERT Solutions |
| Notes | Circles Class 10 Notes |
| Formula Sheet | Circles Formula Sheet |
| NCERT Book PDF | Circles NCERT Book PDF |
| Exemplar Solutions | Circles Exemplar Solutions |
| Exemplar Book PDF | Circles Exemplar Book PDF |
| Handwritten Notes | Circles Handwritten Notes |
NCERT Exemplar Class 10 Maths Circles Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 10 Maths Circles PDF for free?
Ans. You can download the Circles Class 10 Maths NCERT Exemplar Book PDF directly from this page. Both the Normal and HD versions are available, and both are free.
Ques. Is this Circles Exemplar Book aligned with the 2026-27 NCERT syllabus?
Ans. Yes. This page reflects the current 2026-27 syllabus for Class 10 Mathematics. The Exemplar covers tangent-radius perpendicularity, equal tangents from an external point, chord-tangent angle relationships, and two-circle common-tangent configurations.
Ques. How many problems are in the Class 10 Maths Circles Exemplar PDF?
Ans. The Circles Exemplar PDF contains 36 unsolved problems, split as 10 MCQ (Exercise 10.1), 10 reasoning items (Exercise 10.2), 9 short answer (Exercise 10.3) and 7 long answer (Exercise 10.4).
Ques. Is the NCERT Exemplar harder than the NCERT textbook for Circles?
Ans. Yes. The Exemplar introduces multi-step proofs requiring students to name theorems at each step, combined tangent-chord problems, and two-circle common-tangent configurations. This layered style matches the HOTS and long-answer proof questions in recent CBSE Class 10 board papers, which the textbook's direct calculation problems do not fully prepare students for.
Ques. Should I attempt the Circles Exemplar before or after the NCERT textbook?
Ans. Attempt them in parallel. Read the textbook section on a theorem, solve the matching textbook exercise, then attempt the Exemplar problems on the same theorem. Trying the Exemplar first usually leaves students stuck on multi-step proof problems because they have not yet built the single-theorem application habit from the textbook.
Ques. Which Exemplar problems most resemble the CBSE Board long-answer style for Chapter 10?
Ans. The seven long-answer problems in Exercise 10.4 are closest to the CBSE 5-mark proof style. They cover two-tangent proof problems where students must justify each step using named theorems, combined tangent-chord problems requiring angle chasing across two or three steps, and two-circle common-tangent problems where both tangent-radius right angles must be used together.
Ques. What are the key concepts tested in the Circles Exemplar?
Ans. The main concepts tested throughout the Exemplar are: (1) The tangent to a circle is perpendicular to the radius at the point of tangency, (2) The lengths of the two tangents drawn from an external point to a circle are equal, (3) The angle between a tangent and a chord drawn from the point of tangency equals the inscribed angle on the opposite side (alternate segment theorem), (4) Problems with a secant and a tangent from the same external point, (5) Two-circle configurations with common external or internal tangents, and (6) Angle-chasing proofs combining the perpendicularity theorem with properties of isosceles triangles formed by equal tangent lengths.
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